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).

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. An experiment with a fixed volume of gas in a cylinder will reveal the relationship of V vs. T … Temperature scales Is 20  C twice as hot as 10  C? Is 20 kg twice as heavy as 10 kg?

CHARLES' LAW If a gas has a constant mass and is held at a constant pressure then the volume divided by the temperature (in kelvins) is a constant value. V = kT or = k VTVT

Mathematically,

Graphically

Using a glass syringe, a scientist draws exactly 25.5 cm 3 of dry oxygen at 20°C from a metal cylinder. She heats the syringe to 65 °C. What volume will the oxygen occupy? 1.What are you trying to determine? What volume will the oxygen occupy? V f or V 2

Step 2: Identify what is given: V i = 25.5 cm 3 T i = 20.0 °C T f = 65.0 °C

Step 3: Convert temperatures from °C to K T i = 20.0 °CT f = 65.0 °C = 20.0 °C = 65.0 °C = 293 K = 338 K

Step 4: Use equation to determine final volume: = = x 338 K = V f ViTiViTi VfTfVfTf V f V f = cm 3

A balloon is filled with 2.50 L of dry helium at 23.5°C. the balloon is placed in a freezer overnight. The resulting volume is found to be 2.15L. What was the temperature (in °C) in the freezer. 1.What are you trying to determine? What was the temperature (in °C) in the freezer. T f

Step 2: Identify what is given: V i = 2.50 L T i = 23.5 °C V f = 2.15 L Step 3: Convert temperature from °C to K T i = 23.5 °C = 297 K

Step 4: Use equation to determine final temperature: = 2.50 L (T f ) = 297K (2.15L) T f = K ViTiViTi VfTfVfTf T f C ross multiply Divide by 2.50L to isolate T f

Step 5: Convert the temperature back to °C T f = K – 273 = °C

3. A sample of gas occupies 3.5 L at 300 K. What volume will it occupy at 200 K? 4. If a 1 L balloon is heated from 22°C to 100°C, what will its new volume be? V 1 = 3.5 L, T 1 = 300K, V 2 = ?, T 2 = 200K Using Charles’ law: V 1 /T 1 = V 2 /T L / 300 K = V 2 / 200 K V 2 = (3.5 L/300 K) x (200 K) = 2.3 L V 1 = 1 L, T 1 = 22°C = 295 K V 2 = ?, T 2 = 100 °C = 373 K V 1 /T 1 = V 2 /T 2, 1 L / 295 K = V 2 / 373 K V 2 = (1 L/295 K) x (373 K) = 1.26 L