Question

An ideal gas filled in a cylinder occupies volume V. The gas is compressed isothermally to the volume is opened and the gas is allowed to leak keeping temperature same. What percentage of the number of molecules should escape to bring the pressure in the cylinder back to its original value?

• A. 66%
• B. 33%
• C. 0.33%
• D. 0.66%

Answer 1

Answer: (A)

66%

For isothermal compression $\frac{P_1{V}_1}{n_1}=\frac{P_2{V}_2}{n_2}$

$V_2=V_1/3$ , and $P_2=P1$

hence $n_2=\frac{n_1}{3}$

hence $n_1-\frac{n_1}{3}=\frac{2n_2}{3}$

Hence 66.6% gas will escape.