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

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