Question

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius r_A and r_B, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio r_A/r_B is equal to:

Options

• `4/3`

• `3/4`

• `2/sqrt3`

• `sqrt3/2`

Answer 1

`3/4`

Explanation:

From the first law of thermodynamics,

ΔQ = ΔW + ΔU

Since ΔQ and ΔU are the same for both gases,

ΔW_A = ΔW_B

For constant pressure,

ΔW = (PA)x = P(πr²)x

∴ PA_Ax_A = PA_Bx_B

r_A²x_A = r_B²x_B

`(r_A)/(r_B) = sqrt((x_2)/(x_1))`

= `sqrt(9/16)`

= `3/4`