Question

An open vessel containing air was heated from 27°C to 727°C. Some air was expelled. What is the fraction of air remaining in the vessel? (Assume air as an ideal gas)

• A. \( \frac{1}{10} \)
• B. \( \frac{7}{10} \)
• C. \( \frac{3}{10} \)
• D. \( \frac{9}{10} \)

Hint:

In thermodynamics, the fraction of gas remaining can often be found by using the ideal gas law and considering the relationship between pressure, volume, and temperature.

Answer 1

The Correct Option is B

Using the ideal gas law, we know that the pressure and temperature are directly proportional when the volume is constant. The fraction of air remaining can be determined by comparing the initial and final temperatures: \[ \frac{T_2}{T_1} = \frac{V_2}{V_1} \] Where \( T_1 = 27^\circ C = 300K \) and \( T_2 = 727^\circ C = 1000K \). The fraction of air remaining is \( \frac{T_1}{T_2} \), which is \( \frac{7}{10} \).