Question

Three moles of an ideal gas are in a rigid cubical box with sides of length \(0.170\) m. The ratio of the forces that the gas exerts on each of the six sides of the box when the temperature are \(27^\circ\)C and \(127^\circ\)C is

• A. \(5:1\)
• B. \(1:2\)
• C. \(3:1\)
• D. \(3:4\)
• E. \(1:3\)

Hint:

At constant volume, ideal gas pressure is directly proportional to absolute temperature.

Answer 1

The Correct Option is D

For a rigid box: \[ V=\text{constant} \] So for an ideal gas: \[ P\propto T \] Force on a side: \[ F=PA \] Since area \(A\) is constant, \[ F\propto P\propto T \] Convert temperatures into kelvin: \[ 27^\circ\text{C}=300\text{ K} \] \[ 127^\circ\text{C}=400\text{ K} \] Hence, \[ F_1:F_2=300:400=3:4 \] So, \[ \boxed{(D)\ 3:4} \]