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**Problem**: Starting from the relationship between temperature and kinetic energy for an ideal gas, find the value of the molar heat capacity of an ideal gas when its temperature is changed at constant volume.Express your answers in terms of R

###### FREE Expert Solution

At constant volume,

$\mathbf{dU}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{\left(}\frac{\mathbf{\partial}\mathbf{u}}{\mathbf{\partial}\mathbf{T}}\mathbf{\right)}}_{\mathbf{v}}\mathbf{dT}\mathbf{}\mathbf{+}\mathbf{}\mathbf{}\overline{){\mathbf{\left(}\frac{\mathbf{\partial}\mathbf{u}}{\mathbf{\partial}\mathbf{v}}\mathbf{\right)}}_{\mathbf{T}}\mathbf{dV}}\phantom{\rule{0ex}{0ex}}\mathbf{dU}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{\left(}\frac{\mathbf{\partial}\mathbf{u}}{\mathbf{\partial}\mathbf{T}}\mathbf{\right)}}_{\mathbf{v}}\mathbf{dT}\mathbf{}$

where dU = 𝜹q

###### Problem Details

Starting from the relationship between temperature and kinetic energy for an ideal gas, find the value of the molar heat capacity of an ideal gas when its temperature is changed at constant volume.

Express your answers in terms of R

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