# Thermodynamics 1st law question - closed system

1. Oct 27, 2013

### chuffy

1. The problem statement, all variables and given/known data
1kg of helium in a closed system has 40kj added by heating & 100kj removed by work during a reversible polytropic process.
The initial temp of the gas is 300K & the initial pressure is 100kN/m2

Q. find the final temp of the gas & pressure

2. Relevant equations

given: Cp=14.57 kgK & M=4

3. The attempt at a solution

Hi guys, I can't get my head around how to work out the final pressure (P2)

I got the Temp correct (T2) bu doing the following:

R=Ru/M
R =2.0785

Cv = R +Cp
Cv = 7.2715

closed system so V= const

Qnet = -100 -40 =-140
qnet = Q/m

qnet = Cv(T2-T1)
T2 = 281K

Can't think how to work out P2 when I dont have n

any help?

2. Oct 27, 2013

### nil1996

closed system doesn't mean that volume is constant instead it means that the system cannot exchange matter but it can exchange energy.

3. Oct 27, 2013

### physics&math

I'm not entirely sure if this would work, but you could try applying the ideal gas law.

P1V1/T1 = P2V2/T2

Then you would only have to solve for P2. (Since the system is closed, V1 and V2 would cancel).

4. Oct 27, 2013

### nil1996

You have calculated Qnet wrong.Qnet is the net heat change of the system.

5. Oct 27, 2013

### nil1996

Volume is not constant

6. Oct 27, 2013

### chuffy

yeah i've got the const vol bit wong

7. Oct 27, 2013

### Staff: Mentor

You don't know P2 and you don't know n, but you have enough information to solve for both of these. What you need is two equations in these two unknowns.

What is the equation for W in terms of P2 and n for a reversible polytropic process?

What is the equation relating pressure, temperature, and n for a polytropic process?

You already know W and T2.

Chet