Isothermal reversible ideal gas system The concepts deals with system in which the temperature of...
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Transcript of Isothermal reversible ideal gas system The concepts deals with system in which the temperature of...
Isothermal reversible ideal gas system
The concepts deals with system in which the temperature of the system is constant
With the help of this animation user will be able to do expansion and contraction of the system at the constant temperature and check how does the isotherm is plotted
By Rachit AgarwalDepartment of chemistry
IIT Bombay
Instruction for user
temperature
T
pressure
P
volume
V
start
end
Master layout
Pressure tab
Temperature tab
volume tab Heat, change in enthalpy, work and change in internal energy displays
graph
Up and down arrow key
Start and end button
Instruction box
piston weight System thermometer
Heat Q work WChange in enthalpy
Change in Internal energy
1) A constant temperature will be maintained during the process.
1) User can choose a temperature from the list given (this list will be shown in the instruction box)
1) User can change either volume or the pressure and other parameter pressure or volume respectively will be changed by following the law PV= NRT (N=1)
1) The parameter can by changed by using the down and up arrow tabs
1) Both the pressure and volume have their limit pressure 1 to 50 atm, volume from 1 to 50 lts
1) Start button – used to start the process
1) End button – used to stop the process
1) The graph should be plotted simultaneously once the user click the start button till the user presses the end button, even for the change in 0.5 units the graph should be plotted
Instructions for the animator: Working of the animation
select the temperature from the following 150k 300k 450k 600k
start
end
Instructions for the animator: Plotting of the graph
0 10 20 30 40 50
0 10 20 30 40 50
The x axis of the graph is the volume and the y axis of the graph is the pressure
Scale X axis 1 cm = 10 Lts of volumeY axis 1cm = 10 atms of pressure
EgFor P= 25 and V = 4The red dot shows the mark
For P = 2 and V = 50The blue dot shows the mark
And then both the line are joint by a curve line such that the P*V is constant i.e. for the above case P*V is 100 units, so the curve joining both the points should maintain the above relationship as shown in the graph by black curve
Definition and rules for the users
An isothermal is a process in which the temperature is maintained constant during the process, the graph of P v/s V is called as the isotherm at the constant temperature
The change in internal energy in isothermal process is zero (dU = nCvdT)work done is given by integral of –PdV ,
using the first law of thermodynamics the Q (heat) can be calculate as ∆u = Q + w , which implies the Q = -w as change in internal energy change for isothermal process is zero (dU = nCvdT)
the enthalpy can be calculated as H = U + PV , U and PV both are constant , therefore the change in enthalpy is zero for isothermal process
User will read the instruction in the instruction box and then follow the steps as said
It will choose a temperature at which the system process has to be carried
Then he will choose any of the two parameter i.e. pressure or volume and enter the initial value of one of the parameter, the value of the other parameter will come automatically by using the equation PV=nRT , here n =1 , both pressure and volume have limits of 1 to 50 units each
Then the user will click the start button and can change the selected parameter using the arrows tab and reach his final destination and then click the end button to stop the process and to get the values of work, heat, change in internal energy and change in enthalpy
Analogy / Scenario / Action / Example
Volume gradient: the size of the yellow box signifies the volume 100mm = 50lts and The size equal to 2mm = 1ltse.g. Initially yellow box (60mm in height) signifies the volume which is equivalent to 50 units, the finally yellow box (30mm in height) signifies the volume which is equivalent to 25 units
Pressure gradient: the color code (R:G:B 255:0:0) signifies the pressure equal to 1 atm and color code (R:G:B 0:0:0) signifies the pressure equal to 50 atme.g. initially red bar (255:0:0) signifies the pressure = 1atm and finally the bar (127:0:0) signifies pressure = 2 atm
100 m
m
50 m
m
Initial stage Final stage
Instruction for user
Step 1 initial
Action Description Audio narration
enter temperature Allow the user to click the temperature tab
Please click the temperature tab
Circle the temperature tab Once the user clicks the temperature tab Make a yellow circle behind it
click the temperature tab
temperatureT
start
end
Instruction for user
Step 1 final
Action Description Audio narration
enter temperature Allow the user to click the temperature tab
Please click the temperature tab
Circle the temperature tab Once the user clicks the temperature tab Make a yellow circle behind it
click the temperature tab
temperatureT
start
end
Instruction for user
Step 2 initial
Action Description Audio narration
Temperature Allow the user to select the temperature from the list
Please select the temperature from the list in the instruction box
Circle the temperature selected Once the user select the temperature Make a yellow circle behind it and enter that particular value in the box above the temperature tab e.g. 300
select the temperature from the following 150K 300K 450K 600KInstruction for user
temperatureT
start
end
Instruction for user
Step 2 final
Action Description Audio narration
Temperature Allow the user to select the temperature from the list
Please select the temperature from the list in the instruction box
Circle the temperature selected Once the user select the temperature Make a yellow circle behind it and enter that particular value in the box above the temperature tab e.g. 300
select the temperature from the following 150K 300K 450K 600K
temperatureT
start
end
300K
Instruction for user
Step 3 initial
Action Description Audio narration
Select the parameter Allow the user to click either on pressure or the volume tab
Please click the pressure or volume tab , the parameter you want to change
Circle the parameter selected Once the user select the pressure or the volume tab Make a yellow circle behind it E.g. case 1 pressureCase 2 volume
click on the one of the tab from pressure or volume that you want to change
temperatureT
start
end
300K
pressure volume
Instruction for user
Step 3.1 final
Action Description Audio narration
Select the parameter Allow the user to click either on pressure or the volume tab
Please click the pressure or volume tab , the parameter you want to change
Circle the parameter selected Once the user select the pressure or the volume tab Make a yellow circle behind it E.g. case 1 pressureCase 2 volume
click on the one of the tab from pressure or volume that you want to change
temperatureT
start
end
300K
pressure volume
Instruction for user
Case 1 Step 4.1 (pressure) initial
Actionz Description Audio narration
Using the up and down arrow key 1 atm should be displayed as default in pressure tabAllow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab
Range is from 1 atm to 50 atm with 0.5 atm as least count
Click start Allow the user to click the start button e.g the initial value set by the user is 5 atm
set the initial pressure from where you want to start the process using the down and up arrow key, range 1 atm to 50 atm with 0.5 atm as least count then click the start tab to start the process
temperatureT
pressureP
volumeV
start
end
300K
Instruction for user
Case 1 Step 4.1 (pressure) final
Actionz Description Audio narration
Using the up and down arrow key 1 atm should be displayed as default in pressure tabAllow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab
Range is from 1 atm to 50 atm with 0.5 atm as least count
Click start Allow the user to click the start button e.g the initial value set by the user is 5 atm
set the initial pressure from where you want to start the process using the down and up arrow key, range 1 atm to 50 atm with 0.5 atm as least count then click the start tab to start the process
end
`
temperatureT
pressureP
volumeV
5 atm
start
300K
end
Instruction for user
Case 1 Step 5.1 (pressure) initial
Action Description Audio narration
Enter the value of the volume In the box above the volume tab enter the value calculated as (T*.0821/P) lts, in this case it is 4.926
The initial volume is (T*.0821/P) lts(speak the calculate vale) i.e. 4.962 lts
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
The volume is calculated using the equation PV= NRT
end
temperatureT
pressureP
volumeV
5 atm
start
300K
end
Instruction for user
Case 1 Step 5.1 (pressure) final
Action Description Audio narration
Enter the value of the volume In the box above the volume tab enter the value calculated as (T*.0821/P) lts, in this case it is 4.926
The initial volume is (T*.0821/P) lts(speak the calculate vale) i.e. 4.962 lts
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
The volume is calculated using the equation PV= NRT
end
temperatureT
pressureP
volumeV
5 atm
start
300K
4.926 lts
end
Instruction for user
Case 1 Step 6.1 (pressure) initial
Action Description Audio narration
Draw the graph Plot the initial point on the graph , in this case at p= 5 and v = 4.962 by red dot
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab. Eg shown for 0.5 atm change
Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 atm change by blue dotDraw both the points with a black line
Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
end
temperatureT
pressureP
volumeV
5 atm
start
300K
4.926 lts
end
Instruction for user
Case 1 Step 6.1 (pressure) final
Action Description Audio narration
Draw the graph Plot the initial point on the graph , in this case at p= 5 and v = 4.962 red dot
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab. Eg shown for 0.5 atm change
Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 atm change by blue dotDraw both the points with a black line
0 10 20 30 40 50
0 10 20 30 40 50
Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
end
temperatureT
pressureP
volumeV
5.5 atm
start
300K
4.478 lts
end
Instruction for user
Case 1 Step 7.1 (pressure) initial
Action` Description Audio narration
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab.
Value of volume The value of the volume will change every time the pressure is changedBy the formula (T*.0821/P) lts
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is P=50 atm then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm
0 10 20 30 40 50
0 10 20 30 40 50
Your process has started, please change the value of pressure to change the state of the system then click the end button once the process is over
end
temperatureT
pressureP
volumeV
5.5 atm
start
300K
4.478 lts
end
Instruction for user
Case 1 Step 7.1 (pressure) final
Action Description Audio narration
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab.
Value of volume The value of the volume will change every time the pressure is changedBy the formula (T*.0821/P) lts
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is P= 50 atm then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm
0 10 20 30 40 50
0 10 20 30 40 50
Your process has started, please change the value of pressure to change the state of the system then click the end button once the process is over
end
temperatureT
pressureP
volumeV
50 atm
start
300K
0.492 lts
end
Instruction for user
Case 1 Step 8.1 (pressure) initial
Description Audio narration
End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
Value in boxes from heat and work tab
Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Pi/Pf)) J , where Pi is the starting pressure and Pf is the final pressure. And heat as -W E.g. the final pressure by user is 25 atm then the work is =8028.52 J,And heat is -8028.5
Change in internal energy and change in internal energy will be zero because the process is isothermal, the work is (= -8.314*T*ln(Pi/Pf)) and heat is -W
0 10 20 30 40 50
0 10 20 30 40 50
Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
end
temperatureT
pressureP
volumeV
50 atm
start
300K
0.492 lts
end
Instruction for user
Case 1 Step 8.1 (pressure) final
Description Audio narration
End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
Value in boxes from heat and work tab
Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Pi/Pf)) J , where Pi is the starting pressure and Pf is the final pressure. And heat as -W E.g. the final pressure by user is 50 atm then the work is =9757.36 J,And heat is -9757.36 J
Change in internal energy and change in internal energy will be zero because the process is isothermal, the work is (= -8.314*T*ln(Pi/Pf)) and heat is -W
0 10 20 30 40 50
0 10 20 30 40 50
Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over
end
temperatureT
pressureP
volumeV
50 atm
start
300K
0.492 lts
end Heat Q work WChange in enthalpy
Change in Internal energy
0 J0 J-9757.36 J 9757.36 J
Instruction for user
Step 3.2 final
Action Description Audio narration
Select the parameter Allow the user to click either on pressure or the volume tab
Please click the pressure or volume tab , the parameter you want to change
Circle the parameter selected Once the user select the pressure or the volume tab Make a yellow circle behind it E.g. case 1 pressureCase 2 volume
click on the one of the tab from pressure or volume that you want to change
temperatureT
start
end
300K
pressure volume
Instruction for user
Case 1 Step 4.2 (volume) initial
Actionz Description Audio narration
Using the up and down arrow key 1 lts should be displayed as default in volume tabAllow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab
Range is from 1 lts to 50 lts with 0.5 lts as least count
Click start Allow the user to click the start button e.g the initial value set by the user is 5 lts
set the initial volume from where you want to start the process using the down and up arrow key, range 1 lts to 50 lts with 0.5 lts as least count then enter the start tab to start the process
temperatureT
volumeV
pressureP
start
end
300K
end
`
Instruction for user
Case 1 Step 4.2 (volume) final
Actionz Description Audio narration
Using the up and down arrow key 1 lts should be displayed as default in volume tabAllow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab
Range is from 1 lts to 50 lts with 0.5 lts as least count
Click start Allow the user to click the start button e.g the initial value set by the user is 5 lts
set the initial volume from where you want to start the process using the down and up arrow key, range 1 lts to 50 lts with 0.5 lts as least count then enter the start tab to start the process
temperatureT
volumeV
pressureP
300K
5 lts
start
Instruction for user
Case 1 Step 5.2 (volume) initial
Action Description Audio narration
Enter the value of the pressure In the box above the pressure tab enter the value calculated as (T*.0821/V) atm, in this case it is 4.926 atm
The initial pressure is (T*.0821/V) atm(speak the calculate vale) i.e. 4.962 atm
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
The pressure is calculated using the equation PV= NRT
end
temperatureT
volumeV
pressureP
300K
5 lts
start
Instruction for user
Case 1 Step 5.2 (volume) final
Action Description Audio narration
Enter the value of the pressure In the box above the pressure tab enter the value calculated as (T*.0821/V) atm, in this case it is 4.926 atm
The initial pressure is (T*.0821/V) atm(speak the calculate vale) i.e. 4.962 atm
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
The pressure is calculated using the equation PV= NRT
end
temperatureT
volumeV
pressureP
300K
5 lts
start
4.926 atm
Instruction for user
Case 1 Step 6.2 (volume) initial
Action Description Audio narration
Draw the graph Plot the initial point on the graph , in this case at v= 5 and p = 4.962 by red dot
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the pressure tab. Eg shown for 0.5 lts change
Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 lts change by blue dotDraw both the points with a black line
Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
end
temperatureT
volumeV
pressureP
300K
5 lts
start
4.926 atm
Case 1 Step 6.2 (volume) final
0 10 20 30 40 50
0 10 20 30 40 50
Instruction for user
Action Description Audio narration
Draw the graph Plot the initial point on the graph , in this case at v= 5 and p = 4.962 by red dot
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the pressure tab. Eg shown for 0.5 lts change
Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 lts change by blue dotDraw both the points with a black line
Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
end
temperatureT
volumeV
pressureP
300K
5.5 lts
start
4.487 atm
Action` Description Audio narration
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by .5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab.
Value of pressure The value of the pressure will change every time the volume is changedBy the formula (T*.0821/v) atm
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is v= 50 lts then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm
0 10 20 30 40 50
0 10 20 30 40 50
Case 1 Step 7.2 (volume) initial
Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
end
temperatureT
volumeV
pressureP
300K
5.5 lts
start
4.487 atm
0 10 20 30 40 50
0 10 20 30 40 50
Case 1 Step 7.2 (volume) final
end
temperatureT
volumeV
pressureP
300K
50 lts
start
0.492 atm
Action` Description Audio narration
Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by .5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab.
Value of pressure The value of the pressure will change every time the volume is changedBy the formula (T*.0821/v) atm
Change the height of yellow box and colour of piston (bar)
As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide
Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is v= 50 lts then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm
Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
0 10 20 30 40 50
0 10 20 30 40 50
Case 1 Step 8.2 (volume) initial
end
temperatureT
volumeV
pressureP
300K
50 lts
start
0.492 atm Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
Description Audio narration
End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of volume to change the state of the system you can also click on the pressure tab to change the pressure and then click the end button once the process is over
Value in boxes from heat and work tab
Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Vf/Vi)) J , where Vi is the starting volume and Vf is the final volume. And heat as -W E.g. the final volume by user is 50 lts then the work is =-9757.36 J,And heat is 9757.36
0 10 20 30 40 50
0 10 20 30 40 50
Case 1 Step 8.2 (volume) final
end
temperatureT
volumeV
pressureP
300K
50 lts
start
0.492 atm Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over
Description Audio narration
End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of volume to change the state of the system you can also click on the pressure tab to change the pressure and then click the end button once the process is over
Value in boxes from heat and work tab
Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Vf/Vi)) J , where Vi is the starting volume and Vf is the final volume. And heat as -W E.g. the final volume by user is 50 lts then the work is =-9757.36 J,And heat is 9757.36
Heat Q work WChange in enthalpy
Change in Internal energy
0 J0 J9757.36 J - 9757.36 J
Links for further studies
References
books • PETER ATKINS , JULIO DE PAULA – PHYSICAL CHEMISTRY 8TH EDITION
• SIVA PLS ADD SOME BOOKS
Questionnaire
A system started at T=300K and pressure equal to 1atm ,
then the following steps were performed on the system isothermally , calculate the heat, work, change in internal energy, change in enthalpy in each case
Q1) volume is reduced to halfQ2) pressure is doubled Q3) volume is thricedQ4) pressure is taken to 5 atm
`
Answers
A1)a -1728.8,1728.8,0,0b 1728.8,-1728.8,0,0c -1728.8,-1728.8,0,0d 1728.8,1728.8,0,0
A2)a 1728.8,1728.8,0,0B -1728.8,1728.8,0,0c -1728.8,-1728.8,0,0d 1728.8,-1728.8,0,0
A3)a -2740.2,-2740.2,0,0b -2740.2,2740.2,0,0c 2740.2,-2740.2,0,0d 2740.2,2740.2,0,0
A4)a 4014.3,4014.3,0,0b 4014.3,-4014.3,0,0c -4014.3,-4014.3,0,0d -4014.3,4014.3,0,0
The order of the answer is as follows heat, work, change in internal energy, change in enthalpy in each case
Answ
ers
A1
) a
A2) b
A3
) c
A4) d