The pressure and the temperature of an ideal gas in an adiabatic process are related as p prop T^(3). What is the value of the ratio C_(p)//C_(v) of the gas?

The pressure and the temperature of an ideal gas in an adiabatic proce

1.	The pressure and the temperature of an ideal gas in an adiabatic process are related as p prop T^(3). What is the value of the ratio C_(p)//C_(v) of the gas?
Answer» Solution :For 1 mol of an ideal gas, `pV = RT or, T = (pV)/(R )` Now, `p prop T^(3)` or, `p = kT^(3) = k((pV)/(R ))^(2) [k = "constant"]` `:. p = k(p^(3)V^(3))/(R^3) or, p^(2)V^(3) = (R^3)/k` or, `pV^(3//2) = ((R^3)/(k))^(1//2)` or, `pV^(3//2) = "constant"` For an ADIABATIC process, `pV^(gamma)` = constant, So, `gamm = (C_p)/(C_v) = 3/2`