When 100 dm3 of a gas at constant pressure is heated, what is its volume: increase, decrease, same, or except C?

 

When 100 dm3 of a gas at constant pressure is heated, what is its volume: increase, decrease, same, or except C?

Solution

Adding heat to a gas at a constant pressure in a closed system, which means the mass of the system remains constant, will result in change of volume. The ideal gas law, in this case written

PV/T = nR,

and since mass is constant, then nR is constant and the ideal gas law also can be written

P1V1/T1 = P2V2/T2

Because P1 = P2, they divide out of the equation and you are left with

V1/T1 = V2/T2

If the temperature of the gas increases with the added heat, the affect on the volume should be clear, but this assumes that there is a temperature change. If the thermodynamic process is also isothermal, meaning that the temperature also remains constant the 1st law of thermodynamics says that the heat added will equal the work out of the system, Q = -W. Q is heat added to the system and W is work done on the system, so added heat results in negative work, which is work out of the system.

This is generally discussed as a piston/cylinder system and means that the added heat results in the expansion of the gas by doing work of the piston. The end result is a greater volume.