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Charles's Law. The relationship between temperature and volume. How Volume Varies With Temperature . If we place a balloon in liquid nitrogen it shrinks:. So, gases shrink if cooled. Conversely, if we heat a gas it expands (as in a hot air balloon).

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Charles's Law

The relationship between temperature and volume


How volume varies with temperature l.jpg
How Volume Varies With Temperature

If we place a balloon in liquid nitrogen it shrinks:

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.


Temperature scales l.jpg

Is 20C twice as hot as 10C?

Is 20 kg twice as heavy as 10 kg?

Temperature scales

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

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 0C.

  • 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 vs volume graph fig 7 8 pg 430 l.jpg

30

25

20

Volume (mL)

15

10

5

0

100

Temperature (C)

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

25 mL at 22C

31.6 mL, 23.1 mL

Y=0.0847x + 23.137

– 273


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The Kelvin Temperature Scale

  • 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.

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

  • Lord Kelvin suggested that a reasonable temp-erature scale should start at a true zero value.

  • He kept the convenient units of C, but started at absolute zero. Thus, K = C + 273.

    62C = ? K: K=C+273 = 62 + 273 = 335 K

  • Notice that kelvin is represented as K not K.


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Kelvin Practice

Absolute zero is –273C or 0 K

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

Calculate the missing temperatures

0C = _______ K 100C = _______ K

100 K = _______ C –30C = _______ K

300 K = _______ C 403 K = _______ C

25C = _______ K 0 K = _______ C

273

373

–173

243

27

130

298

–273


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Charles’s Law

  • 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:

  • 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


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V1 = 3.5 L, T1 = 300K, V2 = ?, T2 = 200K

Using Charles’ law: V1/T1 = V2/T2

3.5 L / 300 K = V2 / 200 K

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

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

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

V1 = 1 L, T1 = 22°C = 295 K

V2 = ?, T2 = 100 °C = 373 K

V1/T1 = V2/T2,1 L / 295 K = V2 / 373 K

V2 = (1 L/295 K) x (373 K) = 1.26 L

  • Do questions 16, 17, 19 on page 434

For more lessons, visit www.chalkbored.com