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?
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?
How much work is done by the gas during the isothermal contraction?
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!