Finding the heat transferred in an ininitesimal quasistatic process

[Narcol2000]

For an ideal gas PV=nRT where n is the number of moles show that the heat transferred can be written as:

$$dQ = \frac{C_V}{nR}VdP + \frac{C_P}{nR}PdV$$

Really not sure where to start with this...

I have used

$$dQ = dU + PdV$$

But it hasn't really lead anywhere.

 

[Andrew Mason]

For an ideal gas PV=nRT where n is the number of moles show that the heat transferred can be written as:

$$dQ = \frac{C_V}{nR}VdP + \frac{C_P}{nR}PdV$$

Really not sure where to start with this...

I have used

$$dQ = dU + PdV$$

But it hasn't really lead anywhere.

Start with:

dQ = mCdT where C is the heat capacity of the gas. (The heat capacity, of course, depends on whether the gas does work as the heat flows into the gas, so it does not have a fixed value).

Using PV = nRT, what is dT? That should get you going in the right direction.

AM