Adiabatic Process Homework: 2 moles of CO Gas

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SUMMARY

The discussion revolves around an adiabatic process involving 2 moles of carbon monoxide (CO) gas, initially at a pressure of 1.2 atm and a volume of 30 liters, which is compressed to one-third of its volume. The work done during this process is calculated using the formula (P1V1 - P2V2)/(γ - 1), leading to a result of -5032.42 J, which is slightly off from the expected answer of -5100 J. The discrepancy is attributed to potential rounding errors or formula verification, emphasizing the importance of accurate calculations in thermodynamic processes.

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  • Understanding of ideal gas laws and equations
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  • Review the derivation and application of the adiabatic process equations
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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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