An ideal gas is found to obey Pv ^ 3 2 = constant during an adiabatic process. If such a gas initially at a temperature T is aḍiabatically compressed to 1 4 th of its volume, then its final temperature is

Step-by-step solution

Pv ^ 3 2 = constant...(i) Also, PV = nRT p = nRT ~V ...(ii) From eq(i) and (ii), we get ( nRT ~V ) V ^ 3 2 = k T ~V ^ 1 2 = c Now, V₂= V₁ 4 T ₁ ~V ₁^ 1 2 = T ₂ ~V ₂^ 1 2 TV ₁^ 1 2 = T ₂ ( ~V ₁ 4 )^ 1 2 T ₂=2 ~T