In an adiabatic process for an ideal gas, the relation between the universal gas constant ' R ' and specific heat at constant volume ' C _ v ' is R=0 4 C_v . The pressure ' P ' of the gas is proportional to the temperature ' T ', of the gas as T ^k . The value of constant ' K ' is

Step-by-step solution

aligned & P ~T ^ K & PT ^ - K = constant aligned For an adiabatic process, array ll & PT ^ 1- = constant & 1- =- K ...(i) & C _ p = C _ v + R & C _ p = C _ v +0.4 C _ v C _ p =1.4 C _ v & = C _ p C _ v =1.4...(ii) array From(i) and (ii), 1- = 1.4 1-1.4 = -1.4 0.4 = -14 4 = -7 2 aligned & -7 2 =-K & K= 7 2 aligned