IDK y but I cant figure this one out: Two experiments are performed. In the firs
ID: 2097569 • Letter: I
Question
IDK y but I cant figure this one out:
Two experiments are performed. In the first, an ideal gas of N atoms at temperature T(1) in volume V(1) is allowed to expand to a final volume V(f) in an adiabatic, guasi-static process. In the second experiment, which has the same initial conditions, the gas undergoes free espansion to the same final volume. Which experiment causes the greates change in entropy? and why?
I'm thinking one does no work, the other one does so the one doing work has to lose internal energy so the free expansion has to have the greatest change in entropy but part of that does not make sence neither, and I can't prove it mathematically, so any help? thanks
Explanation / Answer
in the first case.... delta Q = 0, hence entropy S= delta Q/T = 0 ......... but in the second case, gas expands from (P1,V1,T) to ( P2, V2,T) , here temperature will not change(expansion would be too fast to exchange the heat) hence entropy will change as following
?S=?dQ/T=?PdV/T=?nRTdV/VT=nR?dV/V=nRln(Vf/Vi