A rigid diatomic gas ( = 7 5 ) is compressed adiabatically to volume ( V_i 32 ) , where V_i is the initial volume. The initial temperature of the gas is ' T_i ' K and the final temperature is ' x ,T_i ' K. The value of x is

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is given by T V^ - 1 = constant . T_i V_i^ - 1 = T_f V_f^ - 1 T_f = T_i ( V_i V_f )^ - 1 Given = 7 5 and V_f = V_i 32 . T_f = T_i (32)^ 7 5 - 1 T_f = T_i (2^5)^ 2 5 T_f = T_i (2^2) = 4 T_i Comparing with T_f = x T_i , we get x = 4 . Answer: 4