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Q.

If 2 moles of an ideal monoatomic gas at temperature $T_{0}$ is mixed with 4 moles of another ideal monoatomic gas at temperature $2 T_{0}$ , then the temperature of the mixture is:

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a

$\frac{3}{2} T_{0}$

b

$\frac{4}{3} T_{0}$

c

$\frac{5}{4} T_{0}$

d

$\frac{5}{3} T_{0}$

answer is A.

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Detailed Solution

$n_{1} = 2; n_{2} = 4$

Let T be the temperature of mixture $U = U_{1} + U_{2}$

$\frac{f}{2} (n_{1} + n_{2}) R T = \frac{f}{2} n_{1} R T_{0} + \frac{f}{2} n_{2} R (2 T_{0})$

$(2 + 4) T = 2 T_{0} + 8 T_{0}$ $T = \frac{5}{3} T_{0}$

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If 2 moles of an ideal monoatomic gas at temperature T0 is mixed with 4 moles of another ideal monoatomic gas at temperature2T0 , then the temperature of the mixture is: