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  • If 2 moles of an ideal monoatomic gas at temperature T are mixed with 3 moles of another monoatomic gas at temperature 2T, the temperature of the mixture will be

If 2 moles of an ideal monoatomic gas at temperature T are mixed with 3 moles of another monoatomic gas at temperature 2T, the temperature of the mixture will be

Option: 1

\mathrm{\frac{8 T}{5}}


Option: 2

\mathrm{\frac{6 T}{5}}


Option: 3

\mathrm{\frac{4 T}{3}}


Option: 4

\mathrm{\frac{3 T}{2}}


Answers (1)

best_answer

Let \mathrm{T_0} be the temperature of the mixture. Since the total internal energy remains
unchanged, we have

\mathrm{U \text { of mixture }=U_1+U_2}

\mathrm{\begin{aligned} & \Rightarrow\left(n_1+n_2\right) C_v T_0=n_1 C_v T_1+n_2 C_v T_2 \\ & \Rightarrow\left(n_1+n_2\right) T_0=n_1 T_1+n_2 T_2 \\ & \Rightarrow(2+3) T_0=2 T+3 \times(2 T)=8 T \end{aligned}}

\mathrm{\text { Which gives } T_0=\frac{8 T}{5}}

Posted by

Rishabh

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