# Adiabatic, Isothermal and Isochoric Processes

## Homework Statement

An ideal gas with Cv = (5/2)R, and Υ = 1.40 undergoes an adiabatic expansion until it has a pressure of 1.0*10^5 Pa and a volume of 2.0m^3. It then undergoes an isothermal contraction of T=300K until it has a volume of 1.0m^3, and then undergoes an isochoric (constant volume) heating until it reaches its original pressure and temperature.

What is Q during the isochoric heating?

## Homework Equations

These are the previous questions that I have already answered and know are correct.

What is the pressure in the gas before the start of the adiabatic expansion?
2.6*10^5 Pa

How much work is done by the gas during the isothermal contraction?
-1.4*10^5 J

## The Attempt at a Solution

At the start of the isothermal contraction (number of moles)-
PV = nRT
n = PV/RT
n = (1.0*10^5)(2.0)/(8.314)(300)
n = 80.19

At the start of the adiabatic expansion (finding final temp for isochoric heating)–
PV = nRT
T = PV/nR
T = (2.6*10^5)(1.0)/(8.314)(80.19)
T = 389.98

For the isochoric heating –

Q = nCvΔT
=(80.19)(5/2)(8.314)(389.98 – 300)
= 1.5*10^5 J

The correct answer is 1.6 * 10^5 J, so I am not really sure where I have gone wrong!

## Answers and Replies

ehild
Homework Helper
You rounded off the initial pressure too early. Keep two more digits.

ehild