Charles’ Law

Temperature Changes & MatterTemperature Changes & Matter

Solids & Liquids expand and contract as Solids & Liquids expand and contract as temperature changes. temperature changes. – Change is usually very smallChange is usually very small

Gases show large volume changes with Gases show large volume changes with temperature changestemperature changes

Jacques CharlesJacques Charles

Balloonist

1787 did experiments showing how volume of gases depends on temperature

How do hot air balloons work?How do hot air balloons work?

Relationship between V and TRelationship between V and TPressure & amount are constant

At high temperature, the gas particles move faster and collide with the walls more often

Pressure is constant, so volume has to increase

Data for Volume-TemperatureData for Volume-Temperature

20220230030055

16716720020044

13213210010033

114114505022

100100101011

Volume (mL)Volume (mL)Temperature (Temperature (C)C)TrialTrial

What did Charles do next?What did Charles do next?

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

0 50 100 150 200 250 300 350

10

50

100

200

300

Linear RelationshipLinear Relationship

Plot Volume vs Plot Volume vs CC and you get a straight and you get a straight line line

The relationship between Volume and The relationship between Volume and C C is is linearlinear

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

0 100 200 300 400 500 600 700

283

323

373

473

573

Charles extrapolated the graph to 0 volume.At 0 mL, the X-intercept is -273 C

Hints of Kelvin scaleHints of Kelvin scale

Charles extrapolated his data to see the Charles extrapolated his data to see the temperature at which the volume was 0temperature at which the volume was 0

This was the first indication that the This was the first indication that the temperature -273 temperature -273 C might have a C might have a fundamental meaningfundamental meaning

Why did Charles have to extrapolate his lines Why did Charles have to extrapolate his lines in this temperature range instead of taking in this temperature range instead of taking data?data?

Plot Volume vs. Kelvin Temp.Plot Volume vs. Kelvin Temp.

Get a straight line that passes through the Get a straight line that passes through the originorigin

The relationship between the variables is The relationship between the variables is directdirect

Charles’ Law:Charles’ Law: Verbal Verbal

The volume of a gas The volume of a gas

at constant pressure at constant pressure

varies directly with varies directly with

its absolute temperatureits absolute temperature

Charles’ Law: Charles’ Law: Graphically Graphically

Plot V vs Kelvin TemperaturePlot V vs Kelvin Temperature

Straight line that passes through the origin Straight line that passes through the origin

V = kT or V = kT or VV = k = kT

Charles’ Law:Charles’ Law: Problems Problems

VV11 = = VV22

T1 T2

Given any 3 variables, you can find the 4th

Problem 1Problem 1

150 mL of a gas at constant pressure150 mL of a gas at constant pressureTemperature increases from 20Temperature increases from 20C to 40C to 40CCWhat is the new volume?What is the new volume?

Step 1:Step 1: Convert T Convert T11 and T and T22 to Kelvin scale. to Kelvin scale.

Step 2:Step 2: Rearrange equation: Rearrange equation:

VV11 = = VV22 becomes becomes VV11TT22 = V = V22

TT11 T T22 T T11

Step 3:Step 3: Substitute and solve: Substitute and solve: 150 mL X 313 K150 mL X 313 K 293 K293 K

= 160 mL

The low temperature region is always extrapolated. Why?

Balloons can expand & contract with the gasBalloons can expand & contract with the gashttp://www.youtube.com/watch?v=IkRIKGN3i0k