The relationship between temperature and

volume

If we place a balloon in liquid

nitrogen it shrinks:

How Volume Varies With Temperature

So, gases shrink if cooled.Conversely, if we heat a

gas it expands (as in a hot air balloon).

Let’s take a closer look at temperature before we try to find the exact relationship of V vs. T.

No. 68F (20C) is not double 50F (10C)

Yes. 44 lb (20 kg) is double 22 lb (10 kg)What’s the difference?• Weights (kg or lb) have a minimum value of 0.• But the smallest temperature is not 0C.• We saw that doubling P yields half the V.• Yet, to investigate the effect of doubling temp-

erature, we first have to know what that means.• An experiment with a fixed volume of gas in a

cylinder will reveal the relationship of V vs. T…

Temperature scalesIs 20C twice as hot as 10C?

Is 20 kg twice as heavy as 10 kg?

Temperature vs. Volume Graph (fig.7,8 pg.430)

5

10

15

20

25

30

Vol

ume

(mL)

Temperature (C) 0 100 – 273

• If a volume vs. temperature graph is plotted for gases, most lines can be interpolated 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.

The Kelvin Temperature Scale

• –273C is known as “absolute zero” (no EK)

• Lord Kelvin suggested that a reasonable temperature scale should start at a true zero value.

• He kept the convenient units of C, but started at absolute zero. Thus, K = C + 273.62C = ? K: K=C+273 = 62 + 273 = 335 K

• Notice that kelvin is represented as K not K.

What is the approximate temperature for absolute zero in degrees Celsius and kelvin?

Calculate the missing temperatures

0C = _______ K 100C = _______ K

100 K = _______ C – 30C = _______ K

300 K = _______ C 403 K = _______ C

25C = _______ K 0 K = _______ C

Kelvin Practice

273 373

– 173 243

27 130

298 – 273

Absolute zero is – 273C or 0 K

• Looking back at the temperature vs. volume graph, notice that there is a direct relationship.

• It can be shown that V/T = constant

Read pages 432-3. Answer these questions:1. Give Charles’s law in words & as an equation.

Charles’s Law: as the temperature of a gas increases, the volume increases proportionally, provided that the pressure and amount of gas remain constant,

V1/T1 = V2/T2

Charles’s Law

2. A sample of gas occupies 3.5 L at 300 K. What volume will it occupy at 200 K?

3. If a 1 L balloon is heated from 22°C to 100°C, what will its new volume be?

4. Do questions 16, 17, 19 on page 434

V1 = 3.5 L, T1 = 300K, V2 = ?, T2 = 200KUsing Charles’ law: V1/T1 = V2/T2

3.5 L / 300 K = V2 / 200 KV2 = (3.5 L/300 K) x (200 K) = 2.3 L

V1 = 1 L, T1 = 22°C = 295 KV2 = ?, T2 = 100 °C = 373 KV1/T1 = V2/T2, 1 L / 295 K = V2 / 373 KV2 = (1 L/295 K) x (373 K) = 1.26 L

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