Question

Derive gamma=mc^2/RT for an ideal gas

derive cp-cv=R

Answer 1

Part A

Adiabatic changes in ideal gases obey the expression PV? = constant

where ? = Cp/Cv

The heat capacity ratio, ?, of a gas can be determined by measuring the speed of sound, c:

? = Mc2/RT

where M is the molecular weight of the gas in kg/mole, c is in meters/second, R is 8.314 J/mol K and T is the absolute temperature.

Part B

Delta(H) = Cp
Delta(U) = Cv
Delta(H) = Delta (U)+Delta(PV) , PV = nRT n = 1 mol
Delta(H) = Delta (U)+R(delta)T
Cp(delta)T = Cv(delta)T + R(delta)T
Cp = (Cv+R) Delta T , {Dividing The Quation By Delta (T)}
Cp = Cv+R
Cp - Cv = R