Matter and Energy. Drill A manometer filled with water is used to measure the pressure of a gas in a...

Matter and Energy

Drill

A manometer filled with water is used to measure the pressure of a gas in a tank. The water (ρ = 1000 kg/m3) is displaced by a height of 60 centimeter. What is the gage pressure of the gas in the tank? What is the absolute pressure?

Matter and Energy

Heat (Q) – energy transfer caused by a temperature difference

Thermodynamics - “the study of systems and energy transfer”

•If we place a flame beneath a system, we would be adding heat to it.•We could also remove heat by surrounding the system with an ice bath.

Matter and Energy

So far, we have defined heat transfer and talked about its sign convention…


…but we haven’t talked about how heat is transferred.

Q in is (+)

Q out is (-)

Matter and Energy

Now let’s talk about the modes of heat transfer (the ways in which heat goes in/out of a system)…


1. Conduction2. Convection3. Radiation

Q in is (+)

Q out is (-)

Matter and Energy

This man is holding one end of a metal rod inside of a furnace with his bare hands. Do you think that he can do that for very long?


Why or why not?Conduction!!!

Over time the rod heats up…

Matter and Energy

Conduction Heat Transfer – energy transfer between molecules due to a temperature difference


The parts of the rod inside the furnace heat up first.

Over time, those molecules pass that heat along to the molecules near them that are outside the furnace.

Eventually the whole rod heats up!

x

TkA- Qcond

(m) distance x,

(K) difference re temperatuT,

)(m area sectional-cross A,

)K-m

W( substance a ofty conductivi k,

(W) ratefer heat trans ,Q

2

Matter and EnergyEnergy is transferred from a warm room at 20C inside a house to the outside air at -10C through a single-pane window. The glass is 5mm thick with an area of 0.5 m2 and a conductivity of 1.4 W/m K. What is the rate of heat transfer through the glass?Known: Heat flows through a window (A=0.5m2, ∆x = 5 mm, k = 1.4

W/m K)Find:

Sketch:

Assumptions: Closed System

Solution:

[W] ,Qcond

condQTroom = 20C = 293 K

Toutside = -10C = 263 K

∆x

x

TkA- Qcond

)(5

263293)m K)(0.5 W/m(1.4- Q

1000

12

cond

mm

mmm

KK

W4200- Qcond

Matter and Energy

The insides of a computer get very hot as it operates. How do we keep them from overheating?


Computers use fans to cool down…just like us!This type of heat transfer is called Convection.

Matter and Energy

Convection Heat Transfer – energy transfer due to the bulk motion of a fluid


As the boards and chips inside the PC heat up, the fan turns on.The fan pulls in cool air from outside the PC which picks up the heat from the boards and chips.The now hot air is forced out of the PC, cooling it down.

ThA Qconv

(K) fluid and surfacebetween difference re temperatuT,

)(m surface of area sectional-cross A,

)K-m

W(t coefficienfer heat trans convection h,


2

2

Matter and EnergyCold air at -10C blows over a warm window-pane with a surface temperature of 12C. The glass has a surface area of 0.5 m2 and the convective heat transfer coefficient is h =100 W/m2 K. What is the rate of heat transfer through the glass?

Known: Heat flows through a window pane (A=0.5m2, 100 W/m2 K)Find:

Sketch:


Solution:

[W] ,Qconv

ThA Qconv

)263285)(m K)(0.5 W/m(100 Q 22conv KK

W1100 Qconv

convQ

Tglass = 12C = 285 K

Toutside = -10C = 263 K

Matter and Energy

The temperature outside changes over time; it’s cool at night and warm throughout the day. Why?


Radiant energy from the sun warms the earth during the day (when the sun is “up”).

Radiant energy leaves the earth during the night, cooling the earth down (when the sun is “down”).

Matter and Energy

The temperature outside changes over time; it’s cool at night and warm throughout the day. Why?


4rad AT Q

(K) re temperatusurface T,

)(m surface of area sectional-cross A,

) (5.67x10constant Boltzmann -Stefan ,

emissivity ,


2

4K-2m

W8-

Matter and EnergyA small light bulb with a surface area of 0.025m2 and an emissivity of 0.6 fluoresces at a temperature of 100C. What is the rate of heat transfer from the light bulb?

Known: Heat radiates from a bulb (A=0.025m2, Tbulb = 100 C, e = 0.6)Find:

Sketch:


Solution:

[W] ,Qrad

W16.5 Qrad

radQ

Tbulb = 100 C = 373 K

4rad AT Q

424K-2m

W-8rad )K (373)m )(0.025 )(5.67x106.0( Q

Matter and Energy


Thermodynamics - “the study of systems and energy transfer”

Conduction

Convection

Radiation

Joules) (J, QQ t

Matter and EnergyA piston cylinder containing a gas was compressed over a period of 20 seconds. The change in energy of the system was 300 kJ and the average rate of heat transfer from the cylinder was 12 kW. Find the work done on the gas in kJ.

Known: A gas is compressed inside of a piston-cylinderFind: W, [kJ]

Sketch:


Solution: 2-12-12-1 W- Q E

2-12-12-1 Q E- W E-t Q W 2-1

kJ/s)(20s) (-12 kJ 300- W 2-1 kJ 540- W 2-1

Q

Matter and Energy

A fan inside of an oven forces hot air to circulate around a turkey to cook it faster.

One half of a metal rod is in the sun and the other half in the shade. You touch the shaded end and notice that it is hot.

On a relatively cool, but very sunny day, you notice that the surface temperature of the sidewalk is above that of the surrounding air.

Identify the type of heat transfer:

Matter and EnergyThe temperature inside of a room with insulated walls is 70C while the outside temperature is 95C. Heat enters the room through a 0.5 m2 window with a thickness and thermal conductivity of 0.05m and 0.3 W/m-K. A portion, 0.4%, of the radiant energy from the sun (e = 0.9, T = 5200 K) enters the room as well.

A student pulls a cart 10m across the floor using a force of 30N; the handle of the cart is at an angle of 60 degrees from the horizontal. How much work is done by the student? How much is done by force of gravity?

Matter and EnergyA vertical piston-cylinder device (D = 5 cm) contains a trapped mixture of gases. The walls of the cylinder are insulated, but heat is allowed to enter through the floor of the cylinder at a rate of 2.75 W over 20 seconds. The absolute gas pressure is 101.3 kPa, initially. If the change in energy of the system is 41 J, how far does the piston rise (in cm) during this process?Known: A gas mixture is heated and expands inside of a piston-cylinderFind: rise of piston, h [cm]

Sketch:

Assumptions: Closed System ,

Solution:

Vertical-piston cylinder -> Isobaric

P

WV

VPW

)V(V P W

2-12-1

2-12-1

122-1

2-12-12-1

2-12-12-1

E - Q W

W- Q E

tQQ

22-1

22-1

πr

V

V

h

hr

32-1

2-1

2-12-1

m 800013.0V

Pa 101.3

14JV

P

WV

k 4J1 W

1J4 - 55J W

E - Q W

2-1

2-1

2-12-12-1

J) 55(Q

)s 02)( W.752(Q

QQ

t

cm 7m 0.07

m) π(0.025

m 800013.0

πr

V

2

3

22-1

h

h

h

Matter and Energy. Drill A manometer filled with water is used to measure the pressure of a gas in a...

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