Adiabatic Process Homework: 2 moles of CO Gas

[mit_hacker]

Homework Statement

2 moles of Carbon monoxide gas start at a pressure of 1.2 atm and a volume of 30 litres. The gas is then compressed adiabatically to 1/3 this volume. Assume that the gas may be treated as ideal. What is the change in the internal energy of the gas? Does the internal energy increase or decrease? Does the temperature increase or decrease?

Homework Equations

PV^γ=constant

W=nC_v dT=nR/(γ-1)(T_2-T_1)

The Attempt at a Solution

The equation for the work done can be re-arranged to give:

(P_1 V_1-P_2 V_2)/(γ-1)

Then, using the equation that PV^γ=constant,

This equation can be "complified" to give:
(P_1 V_1)/(γ-1)[1-〖(V_1/V_2 )〗^(γ-1)

Substituting the values gives: -5032.41775J

The answer given at the back is -5100J.
Can someone please help identify where I went wrong?
Thanks!

 

[Astronuc]

Substituting the values gives: -5032.41775J

The answer given at the back is -5100J.

That seems pretty close, but I haven't checked the formulas. It could be rounding matter somewhere, but there are not values to check.

 

[ogb p]

Your approach and equations are correct. The difference in the answer could be due to rounding errors or different values used for the gas constant (R) and the specific heat at constant volume (Cv). It is also possible that the answer given in the back is an approximation and not an exact value. It is important to note that in an adiabatic process, the internal energy remains constant, so the change in internal energy is zero. The temperature, however, does change as the gas is compressed.