Problem #51[Solved]

You have two containers of the same volume. The container A has a fixed or constant volume, the container B has an expandable/expansible volume. You fill the two containers with air at rtp and close them tightly. You want to heat the air in both containers up to 50^oC.

Question: Will it require the same amount of heat for the two containers, or different amounts of heat? Justify your answer.

Answer: They will require different amounts of heat.

Because, in the fixed volume container A, the heat supplied will be fully utilized to increase the internal energy of the air, ΔU, or its temperature up to 50^oC.

For the expansible/expandable container B, there are two actions: increasing the internal energy, ΔU,  or temperature of air up to 50^oC; but also the volume expansion accomplishes work against the atmospheric pressure, w = -PΔV, where P = atm. pressure, and ΔV= volume expansion. (By convention the work done by a system on its surroundings has a negative sign because it results in a transfer of energy from a system to its surroundings).

In other words, in the expandable container B, a certain amount of internal energy is used to do the expansion work, not to increase the temperature; therefore, it will require more heat for the air in the container B to reach the same temperature of 50^oC.

This explains why cooking in an under-pressure casserole is faster than in an open casserole.