Question

$10$ moles of an ideal monoatomic gas at $ 10^{\circ}\,C $ is mixed with $20$ moles of another monoatomic gas at $ 20^{\circ}\, C $ . Then the temperature of the mixture is

• A. $ 15.5^{\circ}\, C $
• B. $ 15^{\circ}\, C $
• C. $ 16^{\circ}\, C $
• D. $ 16.6^{\circ}\, C $

Answer 1

Answer: (D)

Temperature of the mixture is given by
$T=\frac{n_{1} \,m_{1}+n_{2} \,m_{2}}{n_{1}+n_{2}} $
$T=\frac{10 \times 10+20 \times 20}{10+20}$
$=\frac{500}{30} \approx 16.6^{\circ} \,C$