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Work done (Polytropic Process) watch

    • Thread Starter

    I never know if these are maths or physics questions...

    Basically, I am revising for my mechanical engineering "mechanical science" test, and I've come across this question. When the tutor was going over it, he was vague and didn't know the answer himself... So I have no practice, and whatever practice there is, is bad practice for this question:

    Helium gas expands from 125kPa, 350K, 0.25m^3 to 100kPa in a polytropic process where n=1.667. Find the work done.

    From my notes, W = \frac{mR(T_2 - T_1)}{1-n}  =  \frac{P_2 V_2 - P_1 V_1}{1-n}

    P1 and V1 are stated, as is P2.

    So I use \frac{P_1}{P_2} = \frac{V_2}{V_1} and that gives an end volume, V2, of 0.3125m^3. But, when I stick that into the main equation, the answer comes out as -42kJ, and the answer is 4.09kJ

    The tutor kept explaining some method of doing it with logs, but he didn't even understand what he was writing down. I think this was the second lecture, so I should've gone back and asked (and will do next week if it can't be worked out) because I was utterly confused.

    Any advice?

    • TSR Support Team

    TSR Support Team
    In a polytropic process you should be using P1*V1^n=P2*V2^n=C.
    • Thread Starter

    Well I was given 3 different equations for the polytropic process, and that one did come up too.

    I had a read through what I could find, and I have found the equation they used (made from that equation) but I am not sure how they rearranged the equation to get there...

    V_2 = V_1 (\frac{P_1}{P_2})^\frac{1}{n}

    I really can't see how they got to that stage though.

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