# Ideal gas explanation

1. Mar 13, 2012

### aaaa202

Hi, with the ideal gas law we have:

cp = CV + (∂V/∂T) * P = CV + Nk (constant P)

can someone explain why it intuitively most be so that, the heat capacity at constant pressure is independent of pressure? I mean surely a gas at high pressure wants to expand more?

2. Mar 13, 2012

### Andrew Mason

Perhaps you could explain why you think that heat capacity should be a function of anything - why should it not be constant?

The gas wants to expand more but if you maintain constant pressure it can only so much. How much it expands depends on the change in temperature (pressure being constant): V = nRT/P so ΔV = nRΔT/P. Since the amount of work done at constant pressure is PΔV = P(nRΔT/P) = nRΔT, the amount of work done depends only on the temperature change. The change in internal energy also depends only on the temperature change. This means that the amount of heat flow, Q = ΔU + W = ΔU + PΔV (constant pressure) is proportional to the temperature change (and vice versa ie. temperature change is proportional to heat flow). So Q = CpΔT => dQ/dT = Cp = constant

AM

Last edited: Mar 14, 2012