A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.
Answer (integer)
266
Solution
As work done on gas and heat supplied to the gas are zero,
<br><br>$\therefore$ Total internal energy of gases remain same.
<br><br>u<sub>1</sub> + u<sub>2</sub> = u<sub>1</sub>' + u<sub>2</sub>'
<br><br>We know, $\Delta$U = nC<sub>v</sub>$\Delta$T
<br><br>$\therefore$ $$\left( {0.1 \times {{3R} \over 2} \times 200} \right) + \left( {0.05 \times {{3R} \over 2} \times 400} \right)$$ = $\left( {0.15 \times {{3R} \over 2} \times {T_f}} \right)$
<br><br>$\Rightarrow$ (20 + 20) = 0.15 T<sub>f</sub>
<br><br>$\Rightarrow$ T<sub>f</sub> = 266.67
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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