Compression of an ideal gas

[zulfiqar6]

Homework Statement

An ideal gas, Cp = (5/2)R, Cv = (3/2)R, is changed from P1 = 1 Bar and V₁^t = 12m^3 and V₂^t = 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.

Homework 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

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.

 

[DrClaude]

I know that ΔU = 0 and ΔH = 0

Why is that?

moles aren't given. I can't find any way to get the initial temperature, which is needed for most of the calculations.

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

 

[Andrew Mason]

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

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

 

[DrClaude]

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

Right. Forget my previous comment.

 

[paranormal]

I would like to point out that the problem statement is incomplete and lacks some necessary information to find the solutions. In order to accurately calculate the values of Q, W, ΔU, ΔH and sketch the PV diagram for each process, we would need to know the initial temperature or the number of moles of the ideal gas. Without this information, it is not possible to provide a precise solution to the problem.

Additionally, the equations provided in the problem statement are not entirely correct. For an isothermal process, Q = -W = nRTln(V2/V1), where n is the number of moles of the gas. For adiabatic processes, the equations are given as TV^(γ-1) = const, TP^(1-γ) = const, and PV^γ = const. Also, the equation for isochoric processes should be Q = ΔU = nCvΔT, where ΔT is the change in temperature.

In order to accurately solve this problem, we would need to know the initial temperature or the number of moles of the ideal gas. Without this information, it is not possible to provide a precise solution to the problem. I would suggest revising the problem statement to include all the necessary information for a complete and accurate solution.