Question

If 2 moles of an ideal monoatomic gas at a temperature of 27 °C is mixed with 4 moles of another ideal monoatomic gas at a temperature of 327 °C, then the temperature of the mixture of the two gases is

• A. 300 °C
• B. 227 °C
• C. 233 °C
• D. 327 °C

Hint:

Use mole-weighted averages of temperature (in Kelvin) for mixing ideal gases at different temperatures.

Answer 1

The Correct Option is B

Step 1: Convert temperatures to Kelvin
\[ T_1 = 27 + 273 = 300\, K, \quad T_2 = 327 + 273 = 600\, K. \] Step 2: Calculate final temperature using mole fraction weighted average
\[ T_f = \frac{n_1 T_1 + n_2 T_2}{n_1 + n_2} = \frac{2 \times 300 + 4 \times 600}{2 + 4} = \frac{600 + 2400}{6} = \frac{3000}{6} = 500\, K. \] Step 3: Convert final temperature to Celsius
\[ T_f = 500 - 273 = 227^\circ C. \] Step 4: Conclusion
The temperature of the mixture is 227 °C.