The relation between internal energy `U`, pressure `P` and volume `V` of a gas in an adiabatic processes is : `U = a+ bPV` where a = b = `3` . Calculate the greatest integer of the ratio of specific heats `[gamma]` .

Answer

1

Explanation

For an adiabatic process , `dQ = dU + PdV = 0`
`implies d[a+ bPV] + PdV = 0 implies bPdV + bV dP + PdV = 0 implies (b+1)PdV + bV dP = 0 implies (b+1) (dV)/(V) + b(dP)/(P) = 0`
`implies (b+1) "log"V + b"log"P ` = constant, `V^(b+1)P^(b)` = constant `implies PV^(b+1)/(b) ` = constant `therefore gamma = (b+1)/(b) = (4)/(3) = 1.33`