A `500 Omega` resistor connected to an external battery is placed inside a thermally insulated cylinder fitted with a frictionless pistion. The cylinder contains an ideal gas. A current i of 200mA flows through the resistor as shown in the figure. The mass of the piston is 10kg. Assuming `g = 10m//s^(2)`, the speed at which the piston will move upward, due to heat dissipated by the resistor, so that the temperature of the gas remains unchanged is

Options

A. 10 cm/s
B. 15 cm/s
C. 20 cm/s
D. 30 cm/s

Answer

C

Explanation

As, temperature of gas remains constant, heat supplied by resistance = piston work
`rArr i^(2) Rt = p xx Delta V rArr i^(2) Rt = (F)/(A) xx A xx Delta x`
`rArr (i^(2)R)/(F) = (Delta x)/(t)`= velocity of piston
`rArr v_("piston") = ((200 xx 10^(-3))^(2) xx 500)/(10 xx 10)`
`= (4 xx 10^(-2) xx 5 xx 10^(2))/(10^(2))`
`= 20 xx 10^(-2) ms^(-1) = 20 cms^(-1)`