# Compression of an ideal gas

1. Sep 25, 2013

### zulfiqar6

1. The problem statement, all variables and given/known data
An ideal gas, Cp = (5/2)R, Cv = (3/2)R, is changed from P1 = 1 Bar and V1t = 12m^3 and V2t = 1m^3 by the following mechanically reversible processes:
a) Isothermal compression
b) Adiabatic compression followed by cooling at constant temperature
c) Adiabatic compression followed by cooling at constant volume
d) Heating at constant volume followed by cooling at constant pressure
e) cooling at constant pressure followed by heating at constant volume

find Q, W, ΔU, ΔH, and sketch a PV diagram for each process.

2. Relevant equations

PV=nRT

For isothermal process (a): Q = -W = RTln(V2/V1)

for isobaric processes: Q = ΔH = ∫Cp dT
Adiabatic Processes: TV^(γ-1) = const, TP^(1-γ)/γ = const, PV^γ = const,
for Isochoric processes: Q = ΔU = ∫Cv dT

3. The attempt at a solution

I know that ΔU = 0 and ΔH = 0
moles aren't given. I can't find any way to get the initial temperature, which is needed for most of the calculations.

2. Sep 26, 2013

### Staff: Mentor

Why is that?

Indeed, there is not enough information. Either give results as a function of $n$ or $T$, or assume 1 mole.

3. Sep 26, 2013

### Andrew Mason

Since it is an ideal gas, there is enough information because you can express Q, W, ΔU, ΔH in terms of P1, P2, V1, and V2 using nT = PV/R

AM

4. Sep 27, 2013

### Staff: Mentor

Right. Forget my previous comment.