The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is U = a + bPV where a and b are positive constants. What is the value of gamma ?

The relation between internal energy U, pressure P and volume V of a g

1.	The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is U = a + bPV where a and b are positive constants. What is the value of gamma ?
Answer» `(a)/(b)` `(b+1)/(b)` `(a+1)/(a)` `(b)/(a)` SOLUTION :For an ADIABATIC process, dQ = 0 From the first law of THERMODYNAMICS, we get or `bPdV + bVdP + PdV = 0` or (b+1)PdV + bVdP = 0 or `(b+1) (DV)/(V) + b(dP)/(P) = 0` or `(b+1)(dV)/(V) = -b(dP)/(P)` Integrating both sides, we get (b+1) ln V + b ln P = constant or ln `(V^(b+1)P^(b))` = constant or `PV^((b+1)/(b))` = another constant Compare with the STANDARD equation of an adiabatic process `PV^(gamma)` = constant, we get `gamma = (b+1)/(b)`