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22 \mathrm{~g} of \mathrm{CO}_2 at 27^{\circ} \mathrm{C} is mixed in a closed containers with 16 \mathrm{~g} of  at 37^{\circ} \mathrm{C}. If both gases are considered as ideal kinetic theory gases, then the temperature of the mixture is ____.

Option: 1

28.5^{\circ} \mathrm{C}


Option: 2

30.5^{\circ} \mathrm{C}


Option: 3

31.5^{\circ} \mathrm{C}


Option: 4

33^{\circ} \mathrm{C}


Answers (1)

best_answer


Heat given = Heat taken

\begin{aligned} \therefore n_1 C_{V_1} \Delta T&=n_2 C_{V_2} \Delta T \\ \Rightarrow \frac{1}{2} \times 3 R \times(T-300)&=\frac{1}{2} \times \frac{5}{2} R \times(300-T) \\ \Rightarrow 6 T-1800&=1550-5 T \\ \Rightarrow T&=304.54 \mathrm{~K} \\ & =31.5^{\circ} \mathrm{C} \end{aligned}
 

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Nehul

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