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Calculating specific heat capacity from entropy
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[QUOTE="TSny, post: 6487802, member: 229090"] Looks like you dropped a factor of 3 in getting to the equation ##S = \frac{PV}{T}##. When calculating ##\left(\frac{\partial S}{\partial T}\right)_{P}## you can't treat ##V## as a constant. Likewise when calculating ##\left(\frac{\partial S}{\partial T}\right)_{V}## you can't treat ##P## as a constant. One way to proceed is to find the equation of state that relates the 3 variables ##P##, ##V##, and ##T##. You can then use this to write ##S## as a function of just ##T## and ##P## which then makes it straightforward to evaluate ##\left(\frac{\partial S}{\partial T}\right)_{P}##. Or, you can write ##S## as a function of just ##T## and ##V## so that you can evaluate ##\left(\frac{\partial S}{\partial T}\right)_{V}##. I don't know if this is the best way, but it's one way. [/QUOTE]
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Calculating specific heat capacity from entropy
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