An exam question from 2008 (basic level)
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It is known that the number of moles of an ideal gas is ν, the degrees of freedom of the gas molecules are i, k is the Boltzmann constant, and R is the molar gas constant. When this gas changes from state 1 (P1, V1, T1) to state 2 (P2, V2, T2), the change in its internal energy is ( ). A. νik((t2-t1))/2 B. i((P2V2-P1V1))/2 C. iR(T2-T1)/2 D. νI((P2V2-P1V1))/2 I think the answer to this question is i((P2V2-P1V1))/2
I’ll try to calculate it; I haven’t seen that part yet, hehe
Please provide the solution process; I couldn’t find the formula!
It seems that the internal energy of an ideal gas should be related to temperature and degrees of freedom, and independent of pressure and volume. So when making my choice, I first rule out B and D. Also, I wonder if the options given by the questioner are incorrect; it seems that option C lacks the number of moles of gas, while option A seems to lack Avogadro’s constant. No information available at hand; will check! This post was last edited by winniebear on 2009-2-25 13:14]
First of all, it has been stated that it is an ideal gas; therefore, the internal energy of an ideal gas depends only on temperature. I choose A
Answer B. The process is as follows: the change in internal energy of an ideal gas is ΔU = ivR(T2 – T1)/2, and since PV = vRT, substituting the latter expression into the former will yield the result
Choose B. Why is it P2V2-P1V1 instead of P2V2-P1V2? I think there’s an issue with the answer to this question.