Physics · Ch 8 — Heat and Thermodynamics
Specific Heat Capacity at Constant Pressure and Constant Volume
Specific Heat Capacity at Constant Pressure and Constant Volume
Gases have two distinct specific heat capacities. Specific heat capacity at constant pressure (): the heat needed to raise 1 kg of gas by 1 K while it is free to expand and keep pressure fixed (Figure 8.23); here, part of the supplied heat does external expansion work, and only the remainder raises internal energy. Specific heat capacity at constant volume (): the heat needed to raise 1 kg of gas by 1 K while its volume is held completely fixed by a pin (Figure 8.24), so no work is done at all and all the supplied heat raises internal energy. Because constant-pressure heating must supply extra energy for expansion work on top of raising internal energy, is always strictly greater than . The corresponding molar versions, and (SI unit J mol⁻¹K⁻¹), relate to interna …
What this figure shows. A gas-filled cylinder fitted with a freely movable piston (able to slide against a small pin/stop), enclosed by a conducting wall on one side (through which heat Q is supplied from outside) and an insulator elsewhere. As heat Q flows in, the piston is free to move outward, letting the gas expand to keep the pressure constant while its temperature rises -- illustrating that at constant pressure, part of the supplied heat goes into expansion work, and only the rest …
What this figure shows. The same style of gas-filled cylinder as Figure 8.23, but here the piston is held fixed in place by a pin so it cannot move at all, with heat Q again supplied through a conducting wall. Because the piston cannot move, the gas's volume stays completely fixed as heat flows in, so no work is done at all -- illustrating that at constant volume, ALL of the supplied heat goes directly into raising the internal energy, which is exactly why less heat is needed to achieve the same temperature rise at constan …