Find equation for thermodynamic process

[utkarshakash]

Homework Statement

Find the equation of the thermodynamic process in which specific heat of the gas is given by

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

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.

 

[Chestermiller]

Homework Statement

Find the equation of the thermodynamic process in which specific heat of the gas is given by

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

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.

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

Chet

 

[utkarshakash]

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

Chet

No. It's a positive constant.

 

[Tanya Sharma]

Hi utkarshakash

I can write

$C=C_v + \alpha P$

Correct...

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.

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 C_P or C_V .

Apply the first law of thermodynamics .

 

[utkarshakash]

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 C_P or C_V .

Apply the first law of thermodynamics .

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?

 

[Tanya Sharma]

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

where m=mass of gas

I think it should be

nCdT = nC_VdT + pdV

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

 

[utkarshakash]

I think it should be

nCdT = nC_VdT + pdV

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

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

 

[Tanya Sharma]

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

ΔQ=nCΔT is applicable in every process.

 

[utkarshakash]

ΔQ=nCΔT is applicable in every process.

Thanks. I got the correct answer.