Cv is given by
A. $${\left( {\frac{{\partial {\text{E}}}}{{\partial {\text{T}}}}} \right)_{\text{V}}}$$
B. $${\left( {\frac{{\partial {\text{E}}}}{{\partial {\text{V}}}}} \right)_{\text{T}}}$$
C. $${\left( {\frac{{\partial {\text{E}}}}{{\partial {\text{P}}}}} \right)_{\text{V}}}$$
D. $${\left( {\frac{{\partial {\text{V}}}}{{\partial {\text{T}}}}} \right)_{\text{P}}}$$
Answer: Option A
Solution (By Examveda Team)
Definition of $${C_V}$$ : when we add the heat to a system which is undergoing only expansion work or $$PdV$$ work at constant volume than the amount of heat required to raise the temperature by an infinitesimal amount is called as $${C_V}$$.$${C_V} = \mathop {\lim }\limits_{\delta T \to \,0} \frac{{\partial Q}}{{\partial T}}$$
By first law of thermodynamics: $$\delta Q = dU + \delta W\left( {PdV} \right)$$ Since here $$dV=0$$
$$\delta Q = dU$$
So, $${C_V} = {\left( {\frac{{dU}}{{dT}}} \right)_V}.$$ Where $$U=$$ internal energy.
This Question Belongs to Chemical Engineering >> Chemical Engineering Thermodynamics
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