Heat Capacities

Heat Capacities

Basic Definition

Heat Capacity at Constant Volume ($dV = 0$)

$$ \large \begin{split} dU &= dQ - pdV \\ &= \frac{3}{2} nRdT \end{split} $$$$ \large \Rightarrow C_V = \left( \frac{dQ}{dT} \right)_V = \frac{3}{2}nR $$

Heat Capacity at Constant Pressure ($dP = 0$)

$$ \large dU = dQ - pdV $$$$ \large dQ = dU + pdV = \frac{3}{2}nRdT + nRdT $$$$ \large \Rightarrow C_P = \left( \frac{dQ}{dT} \right) = \frac{5}{2} nR $$

Relationship between $C_P$ and $C_V$

$$ \large C_V < C_P $$
  • GRE Physics GR0877: Problem 034

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