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Which $ONE$ of the following is $CORRECT$ for an ideal gas in a closed system?

- $\left ( \frac{\partial U}{\partial V} \right )_{s}V=nR\left ( \frac{\partial U}{\partial S} \right )_{V}$
- $-\left ( \frac{\partial H}{\partial P} \right )_{s}P=nR\left ( \frac{\partial H}{\partial S} \right )_{P}$
- $\left ( \frac{\partial U}{\partial V} \right )_{s}V=nR\left ( \frac{\partial H}{\partial S} \right )_{P}$
- $\left ( \frac{\partial H}{\partial P} \right )_{s}P=nR\left ( \frac{\partial U}{\partial S} \right )_{V}$