A monatomic gas at 630 ~K expands adiabatically to 27 times its initial volume. The final temperature of the gas is

Step-by-step solution

For mono-atomic, f =3 =1+ 2 f = 5 3 For adiabatically PV ^ = constant aligned & ( PV = n RT ) & ( nRT V ) V ^ = constant & T ₁ ~V ₁ ^ -1 = T ₂ ~V ₂ -1 & 630( ~V )^ -1 (27 ~V )^ -1 = T ₂ aligned Final temperature of gas, T₂= 630 (27)^ -1 = 630 (3)^ 3 5 3 -1 =70 ~K