# Homework Help: Find equation for thermodynamic process

1. May 3, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
Find the equation of the thermodynamic process in which specific heat of the gas is given by

$C=\dfrac{R}{\gamma -1} + \alpha P$

3. The attempt at a solution

I can write

$C=C_v + \alpha P$

But I don't know how to proceed ahead. What does C mean here? Is it specific heat capacity at constant pressure or volume? Any help is appreciated.

2. May 3, 2014

### Staff: Mentor

Is α supposed to be the coefficient of volumetric thermal expansion? Because, if it is, it's units are wrong.

Chet

3. May 3, 2014

### utkarshakash

No. It's a positive constant.

4. May 3, 2014

### Tanya Sharma

Hi utkarshakash

Correct...

C is the specific heat capacity of the process .It is neither of the two (i.e at constant pressure or volume ) .It is not that the heat capacity has to be either CP or CV .

Apply the first law of thermodynamics .

5. May 3, 2014

### utkarshakash

I get
$m(C_v + \alpha P) dT = nC_vdT + \int P dV$

where m=mass of gas
How do I calculate the work done in the process?

6. May 3, 2014

### Tanya Sharma

I think it should be

nCdT = nCVdT + pdV

Write Cv in terms of C and take n =1 for sake of simplicity.

7. May 3, 2014

### utkarshakash

But ΔQ=nCΔT is valid only when C=Cp. In general ΔQ=mCΔT

8. May 3, 2014

### Tanya Sharma

ΔQ=nCΔT is applicable in every process.

9. May 3, 2014

### utkarshakash

Thanks. I got the correct answer.