One mole of a perfect gas, initially at a pressure and temperature of 10 5 N m - 2 and 300 K , respectively, expands isothermally until its volume is doubled and then adiabatically until its volume is again doubled. Find the final pressure of the gas. Given γ = 1.4 .

Step-by-step solution

Let P 1 ,   V 1 ,   T 1 be the initial pressure, volume and the temperature of the gas, respectively. For isothermal expansion (1 to 2), we have     V 2   =   2 V 1   ;     P 1 V 1   =   P 2   V 2     P 2   =   P 1 V 1 V 2   =   P 1 2   =   0 . 5   ×   10 5   N   m - 2       T 2   =   T 1   =   300   K For adiabatic expansion (2 to 3), P 2 V 2 γ =