In thermodynamics, the equation relating pressure P, volume V, number of moles N, and temperature T is given by PV = NRT where R is Avogadro’s constant.
a) Show that PdV + VdP = NRdT.
b) Using the adiabatic condition dU = –PdV and the energy equation dU = NcvdT where U is the total energy and cv is the molar heat capacity, show the differential equation in part (a) can be expressed as
PdV + VdP = –(R/cv)PdV.
c) Solve the differential equation in part (b) to obtain the equation for the ideal gas process relating P and V.
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