How to Calculate Energy and Work in a Stirling Cycle?

[mathpialpha]

Homework Statement

Suppose that 282 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.81 m^3 at a temperature of 574 K. The piston is connected to a hot reservoir with a temperature of 1365 K and a cold reservoir with a temperature of 574 K. The gas undergoes a quasi-static Stirling cycle with the following steps:

1. The temperature of the gas is increased to 1365 K while maintaining a constant volume.
2. The volume of the gas is increased to 3.13 m^3 while maintaining a constant temperature.
3. The temperature of the gas is decreased to 574 K while maintaining a constant volume.
4. The volume of the gas is decreased to 0.81 m^3 while maintaining a constant temperature.

It may help you to recall that C_V = 12.47 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 × 10^23) times the number of moles of the gas.

1) What is the pressure of the gas under its initial conditions?
I got this question correct and it is 1661921.138 Pa

2) How much energy is transferred into the gas from the hot reservoir?

3) How much energy is transferred out of the gas into the cold reservoir?

4) How much work is done by the gas during this cycle?

5) What is the efficiency of this Stirling cycle?

6) What is the maximum (Carnot) efficiency of a heat engine running between these two reservoirs?
I got this question correct and it is 0.579487

I need help with questions #2-5

Homework Equations

Q_H = Q_C + W_(By Engine)
PV =NKT
work = NK*T_H*ln(Vbig/Vsmall)
Q_H = C_v(T_H - T_C) + work

The Attempt at a Solution

I got questions #1 and #6 correct. I tried using the equations above for the other problems but I cannot get the correct answer[/B]

 

[Gianmarco]

You should write your attempts at solving the problem else it's difficult to understand your mistake and point you in the right direction. Also your equation for work in an isothermic is wrong. ##W=Q=nKTln\frac{V_f}{V_i}##, where ##V_f## and ##V_i## are final and initial volumes of the isothermic.

 

[mathpialpha]

You should write your attempts at solving the problem else it's difficult to understand your mistake and point you in the right direction. Also your equation for work in an isothermic is wrong. ##W=Q=nKTln\frac{V_f}{V_i}##, where ##V_f## and ##V_i## are final and initial volumes of the isothermic.

For Question 2, I used Q_H = C_v(T_H-T_C) + NkT_H*ln(Vbig/Vsmall) and got 4337132.48 J

 

[Gianmarco]

For Question 2, I used Q_H = C_v(T_H-T_C) +...

You're not accounting for the number of moles in your expression for the change of internal energy of the system