Two moles of an ideal monoatomic gas occupy a volume V at 27^(@)C. The gas expands adiabatically to a volume 8V. Find the change in internal energy of the system. [Given C_(V) = (3R)/(2)J mol^(-1).^(@)C^(-1)]

Two moles of an ideal monoatomic gas occupy a volume V at 27^(@)C. The

1.	Two moles of an ideal monoatomic gas occupy a volume V at 27^(@)C. The gas expands adiabatically to a volume 8V. Find the change in internal energy of the system. [Given C_(V) = (3R)/(2)J mol^(-1).^(@)C^(-1)]
Answer» Solution :For an adiabatic change, `TV^(gamma -1)` = constant `:. (T_(2))/(T_(1)) = ((V_(1))/(V_(2)))^(gamma - 1) = ((V)/(8V))^((5)/(3)-1) = ((1)/(8))^(2//3)` Here, `gamma = (5)/(3)` monoatomic gas `= ((1)/(2^(3)))^(2//3) = ((1)/(2))^(2) = (1)/(4)` or `T_(2) = (T_(1))/(4) = ((273 + 27))/(4) = (300)/(4) = 75 K` Now, `Delta U = nC_(V)dT` or `Delta U= 2 xx (3R)/(2) xx (75 - 300) = 3 xx 8.3 xx (-225) = 5602.5 J`