1. Volume and Temperature
Charles’s Law
Volume and Temperature

2. How Volume Varies With Temperature
If a balloon is placed in liquid nitrogen it shrinks:
So, gases shrink if cooled.
Conversely, if we heat a gas it expands (as in a hot air balloon).

3. Temperature Scales Is 20o C twice 10o C ? Is 20 kg twice 10 kg?
NO. 20o C = 68 oF or 293 Kelvin
10oC = 50 oF or 283 Kelvin
Is 20 kg twice 10 kg?
YES. 20 kg = 44 lbs; 10 kg = 22 lbs
What’s the Difference?
Weight has a minimum of zero, but oC doesn’t
We use Kelvin for Charles’s law because 0 Kelvin equates to zero molecular movement

4. Temperature vs. Volume Graph5 10 15 20 25 30
Volume (mL)
Fixed Volume in a cylinder
25 mL at 22C
31.6 mL, 23.1 mL
Y=0.0847x
Temperature (C)
100
– 273

5. The Kelvin Temperature Scale
If a volume vs. temperature graph is plotted for gases, most lines can be interpreted so that when volume is 0 the temperature is -273 C.
Naturally, gases don’t really reach a 0 volume, but the spaces between molecules approach 0.
At this point all molecular movement stops.
–273C is known as “absolute zero” (no EK)
Kelvin kept the convenient units of C, but started at absolute zero. Thus, K = C
62C = ? K: K=C+273 = = 335 K
Notice that Kelvin is represented as K not K.

6. Temperature MUST be in KELVIN
Charles’s Law
Looking at the temperature vs volume graph, we can see that:
If temperature increases, volume increases
If temperature decreases, volume decreases
Charles’s Law: V = bT
(b is a proportionality constant)
So… b/ = V/T b
b = V1/T1 and b = V2/T2
V1/T1 = V2/T2
Temperature MUST be in KELVIN

7. Calculating Volume using Charles’s Law
A 2.0-L sample of air is collected at 298 K and then cooled to 278 K. The pressure remains constant at 1.0 atm.
Does the volume increase or decrease?
Since the ratio of V/T = b, if T is decreased then V must also decrease so that the constant remains the same
Calculate the volume of air at 278 K
Initial Conditions Final Condiitions
V1 = 2.0 L V2 = ?
T1 = 298 K T2= 278 K
2.0/298 = V2/278
V2 = (278)(2.0/298)
V2 = 1.9 L

8. Calculating Temperature
In former times, gas volume was used as a way to measure temperature using gas thermometers. Consider a gas with a volume of L at 35o C and constant pressure of atm. What is the temperature (in oC) of a room where this gas has a volume of L ?
Initial Conditions Final Condiitions
V1 = L V2 = L
T1 = 35o C T2= ?
( = 308 K)
Then divide by to get:
T2 = 0.535/(0.675/308)
So T2 = 244 K
0.675/308 = 0.535/T2
Divide both sides by T2 to get:
T2(0.675/308) = 0.535
244 – 273 = -29o C

9. Charles’s Law Practice:
V = 1.14 L at 21o C; what is the volume at 42o C
V = 257 mL at 45o C; V = 300 mL at ? o C
V = 2.78 L at -50o C; V = 5.00 L at ? o C
V = 73.5 mL at 0o C; V = ? at 25o C
Suppose 1.25 L of argon is cooled from 291 K to 78 K. What will the new volume of argon be?
Aerosol cans should be stored within a specific temperature range because they are pressurized. Calculate the potential volume of the gas contained in a 500mL can when it is heated from 25o C to 54o C.
Suppose a 25.2 mL sample of helium gas at 29o C is heated to 151o C. What will the new volume of the helium sample be?
Suppose a gas sample is cooled from 600 K to 300 K. Describe how the new volume of gas would relate to the original volume of gas.