The constant volume molar heat capacity of an ideal gas is expressed by `C_(v, m) = 16.5 +10^(-2)T` (All values are in SI units). If 2.5 mol of this gsa at constant value is heated from `27^(@)C` ro `127^(@)C`, the internal energy increases by ''x'' kJ. Hence, x is

Answer

5

Explanation

`Deltau= underset(T_(1))overset(T_(2))(int)nc_(v)dT=n underset(T_(1))overset(T_(2))(int) adT+bTdT`
`Deltau=na(T_(2)-T_(1))+(nb)/(2) (T_(2)^(2)-T_(1)^(2))`
Given `C_(vm)=a +bT=16.5+10^(-2) T`