Question

How much energy would be required to heat two moles of methane by one degree if the gas is kept at constant volume?

Answer 1

$Molar\ Heat\ Capacity\ at\ constant\ Volume\ = \\ \ \ C_v of methane (CH_4) = 27.1 J K^{-1} mol^{-1}, \ \ \ \ \gamma = 4/3 \\ \\ Energy = n C_v \Delta\ T =\ 2\ moles\ *\ 27.1 J\ K^{-1}\ mol^{-1}\ *\ 1 degK \\ \\ \ \ =\ 54.2 J$

The work done is zero by the pressure as the volume is kept constant. The energy goes goes into heating the gas and that goes as the Internal energy in the gas.