The work done by a gas may always be calculated by the following equation: (For
ID: 2210998 • Letter: T
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The work done by a gas may always be calculated by the following equation: (For integration here, I will use the symbol "S" and take up 3 lines.) (for subs I use [ ] ) Key: i= initial, f = final, R = ratio of heat capacities V[final] W= S P(V)dV V[initial] In an adiabetic process, where the equation implies P=P[i]*V[i]/V[R] Obtain the following equation and show work W=(P[i]*V[i]/(R - 1))*(1-(V[i]/V[f])^([R]-1])) I don't know where to start with this, could you please explain the integration process and how I should go about doing it?Explanation / Answer
for adiabatic process PV^(gamma) = constant take constant as C. so P = C*V(-gamma), work = integral P*dv work = C*V^(-gamma ) * dv integration gives: work = C*V^(1- gamma)/(gamma -1 ) work = (PV^(gamma))/(gamma -1 ) put limits from 1 to 2 you will get work done in adiabatic proces
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