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Heat Capacity

If 4 moles of...

Question

If 4 moles of an ideal monatomic gas at temperature 400K is mixed with 2 moles of another ideal monatomic gas at temperature 700K, then the temperature of the mixture is:
(Volume is assumed constant)

550^{o} C

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500K

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550K

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536K

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Solution

The correct option is C 500K
When both the monoatomic gases are mixed:
$(n_{1} + n_{2}) T = n_{1} T_{1} + n_{2} T_{2}$
$T = \frac{n_{1} T_{1} + n_{2} T_{2}}{n_{1} + n_{2}} = \frac{4 (400) + 2 (700)}{(4 + 2)} = 500 K$

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