Specific heat and degrees of freedom

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Question

A non-conducting partition divides a container into two equal compartments. One is filled with helium gas at 200 K and the other is filled with oxygen gas at 400 K. The number of molecules in each gas is the same. If the partition is removed to allow the gases to mix, the final temperature (in K) will be

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Solution

$\begin{array}{l} Conservation of energy, \\ n (\frac{3 R}{2}) (200) + n (\frac{5 R}{2}) (400) = n (\frac{3 R}{2}) T + n (\frac{5 R}{2}) T \\ \Rightarrow T = \frac{600 + 2000}{8} = 325 K \end{array}$

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Specific heat and degrees of freedom

Remember concepts with our Masterclasses.

Conservation of energy,n(3R2)(200)+n(5R2)(400)=n(3R2)T+n(5R2)T⇒T=600+20008=325K

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$\begin{array}{l} Conservation of energy, \\ n (\frac{3 R}{2}) (200) + n (\frac{5 R}{2}) (400) = n (\frac{3 R}{2}) T + n (\frac{5 R}{2}) T \\ \Rightarrow T = \frac{600 + 2000}{8} = 325 K \end{array}$