Question

prove that pvr =constant​

Answer 1

We know that from 1st law of thermodynamics law

dQ=dU+dW

From adiabatic process we can say dQ=0

so, dU+dW=0= dU+pdV.....(1)

we know that dU= nCvdT.....(2)

from ideal gas equation PV=nRT (or) dT=PdV+VdP÷nR

by putting it in eq-2, we get

dU=Cv(PdV+VdP)÷R

putting this value of dU in eq-1 we get

dP÷P= -dV÷V(Cv+R÷Cv)

so if we integrate it we get

PVgama=constant