Thermodynamic Cycle, Balloon Volume, and Cooling Effects

1. P V 90 In the closed thermodynamic cycle shown in the P-V diagram, the work done by the gas is • Positive. • Zero. • Negative.

2. 60 What happens to the volume of a balloon if you put it in the freezer? • The volume increases. • The volume decreases. • The volume stays the same.

3. 60 A plastic soda bottle is empty and sits out in the sun, heating the air inside. Now you put the cap on tightly and put the bottle in the fridge. What happens to the bottle as it cools?. • It expands (and may burst). • It stays the same. • It contracts (and the sides may collapse).

4. Answers • 1, the gas does positive work here, since the expansion (when the gas does work on the piston) happens at the higher pressure, so W=PDV is larger than the lower leg when the piston does work on the gas to compress it. If the arrows went the other way, then the gas would be compressed by the piston at the higher pressure meaning that the larger work is done by the piston. • 2. The gas in the balloon cools in the freezer (heat leaves) meaning T is lower. If the pressure on the balloon is constant, then the Volume must decrease to satisfy PV=nRT. In this case, the pressure actually decreases some too, since the pressure is determined by the stretchiness of the balloon itself (think Hooke’s Law F=-kx). So, the temp decreases making the Volume decrease, and this then reduces the pressure too (since the balloon is not stretched as far). So, both P and V go down to match the decrease in T. • 3. Again the gas cools reducing T. This reduces the pressure in the plastic bottle since at least initially the plastic is strong enough to remain rigid. Eventually the pressure inside can become low enough that the difference in pressure between the inside and outside of the bottle is enough force to collapse the bottle.