Is the Heat Capacity of Thermal Radiation at Constant Pressure Infinite?

[sachi]

we need to show that the heat capacity of thermal radiation at constant pressure is infinity. I have an argument, but am not sure if it works. we know that Cp = dQ/dT at constant p, but we also know that p is a function of T only, and therefore that T is a function of P only, therefore if dP=0,dT=0, so the denominator of Cp is zero and Cp is infinite. we are then asked to interpret this. I think it means that adding energy or subtracting it makes no difference to temperature if the pressure is constant, i.e thermal radiation acts as a heat resevoir at constant P, or does it mean that we can't add/subtract energy at constant temperature?

thanks

 

[Zassounotsuku]

Similar problem here. I'm conflicted by considering the release of energy into a volume of space. If you assume reflective boundary conditions, then I think the space could be taken to have some specific heat. I would like to know how to effectively calculate that.