Question

Gases

Answer 1

The equation of state of a gas is given by\[V = \frac{RT}p - \frac{b}T\]where \(R\) is the gas constant and \(b\) is another constant parameter. The specific heat at constant pressure \(C_P\) and the specific heat at constant volume \(C_V\) for the gas is related by the relation \(C_P - C_V = \cdots\)

Answer 2

\[C_m = \frac{dQ}{dT} = \frac{dU + dw}{dT} = \frac{dU}{dT}+p\frac{dV}{dT}\]\[C_V = \frac{dU}{dT} ~\rm since ~dV=0.\]\[\Rightarrow C_m =C_V + p\frac{dV}{dT}\]

Answer 3

\[\frac{dV}{dT} = \frac{R}p+\frac{b}{T^2}\]\[p\frac{dV}{dT}=R+\frac{pb}{T^2}=C_P-C_V \]

Answer 4

where did I go wrong

Answer 5

I've treated \(p\) as a constant parameter which it is.

Answer 6

http://imgur.com/Srqgwer

Answer 7

(C) is pretty close to my answer except there's a squared term.

Answer 8

yeah removing that 2 in the exponent matches with your answer

Answer 9

the problem is we can't dimensionally verify this either, because the terms multiplied to \(R\) are dimensionless.

Answer 10

Hey ganeshie is it possible to use the given equation of state and manipulate the answer?

Answer 11

Certainly got my definitions wrong somewhere along the way... >_<