Adiabatic Process Homework: 2 moles of CO Gas

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The homework involves calculating the change in internal energy of 2 moles of carbon monoxide gas compressed adiabatically from a volume of 30 liters to 10 liters at an initial pressure of 1.2 atm. The relevant equations include PV^γ=constant and work done W=nC_v dT. The attempt at a solution yields a work done of -5032.42 J, which is close to the provided answer of -5100 J, suggesting a potential rounding issue. The discussion highlights the need to verify calculations and formulas used in the process. Understanding the implications of adiabatic compression indicates that the internal energy decreases and the temperature increases.
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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!
 
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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.
 

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