Undergrad PV^K = C; K is always the same for a given gas, is the same true for C?

[timsea81]

For an ideal gas, PV^K=C, where C is some constant and K is the ratio of the specific heats. K is obviously the same in all cases (all samples of helium have the same value of K, for example). Is the same true for C?

If you have 2 samples of the same gas, can the values of C be different for each if they are at different temperatures? What if they are at the same temperature?

 

[Ken G]

PV^K = C holds when you have adiabatic expansion/compression of the gas. Therefore C cannot depend on T, because T changes in adiabatic expansion/compression. But it can't always be the same for some gas either, because if it were, if I told you the gas and what its pressure was, you would then know its volume, which certainly isn't true, even about the air around you. So C is neither a global constant, nor a function of T, it must depend on something else that is situation-dependent. Since adiabatic expansion means expansion at constant entropy, C must relate to the entropy of the gas.

 

[electrous]

for any gas before compression and after compression their specific heat ratios remains constant because we are considering the same gas at the one moment. so as long as we are treating same gas or substance it remains constant.

 

[Philip Wood]

To start off-topic, in the isothermal case, PV = constant. Here the constant has a very neat interpretation. It is equal to nRT, so it is proportional to the kelvin temperature.

Now consider the adiabatic case, where PV^\gamma = C. This is one curve of a family, with different family members having different values of C. Unlike the isothermal case, C has no neat interpretation, it is simply the value of PV^\gamma along a particular curve. You could think of it as set by the initial values P₀ and V₀ and equal to, P₀V₀^\gamma.

You were interested in relating C to T? All you can do is express C in terms of P and T or V and T instead of P and V. Let's go for V and T. Using the ideal gas equation:

C = PV^\gamma = nRT V^{(\gamma - 1)}.

So C for a particular adiabatic curve isn't determined uniquely by the initial value of T; it depends also on the initial V. During the course of the adiabatic change, both T and V change such that nRT V^{(\gamma - 1)} remains constant.

Any help?