Question

Two identical containers A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The mass of gas contained in A is and that in B is . The gas in each cylinder is now allowed to expand isothermally to the same final volume 2V. The change in the pressure in A and B are found to be and 1.5 respectively. Then

• A. 4 = 9
• B. 2 = 3
• C. 3 = 2
• D. 9 = 4

Answer 1

Answer: (C)

3 = 2

Answer 2

For gas in A,

$\therefore$ $\Delta \mathrm { P } = \mathrm { P } _ { 2 } - \mathrm { P } _ { 1 } = \left( \frac { \mathrm { RT } } { \mathrm { M } } \right) \mathrm { m } _ { \mathrm { A } } \left( \frac { 1 } { \mathrm {~V} _ { 1 } } - \frac { 1 } { \mathrm {~V} _ { 2 } } \right)$

Putting $V _ { 1 } = V$ and $V _ { 2 } = 2 \mathrm {~V}$

We get$\Delta \mathrm { P } = \left( \frac { \mathrm { RT } } { \mathrm { M } } \right) \frac { \mathrm { m } _ { \mathrm { A } } } { 2 \mathrm {~V} }$

Similarly for Gas in B,

From eq. (I) and (II) we get 2 = 3

Hence (3) is the correct.