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# JEE Class main Answered

In figure, a resistance coil, wired to an external battery is placed inside a thermally insulated cylinder find with a frictionless piston and containing an ideal diatomic gas A current = 200 ma exists in the coil which has a resistance R=350Ω If the pressure of the gas remains constant what should be the speed v (in cm/s of the piston of mass m=10kg)?
Asked by samarthghogare | 06 May, 2023, 11:17: AM
Let us assume the dissipated heat in the resistance coil is absorbed by the enclosed gas in the cylinder.

Rate of heat dissipation is

...................... (1)

where i is current through coil and Rc is resistance of coil .

For diatomic gas that is hetaed at constant pressure , heat dissipation is

.............................. (2)

where n is number of moles , Cp =(7/2) R  is constant volume specific heat, R is universal gas constant  and
(dT/dt) is rate of change of increase of temperature.

From eqn.(1) and eqn.(2), we get

......................... (3)

For ideal gas , we have

when pressure is kept constant , rate of change of volume is

Above expression can be written as

............................. (4)
where A is area of cross section of cylinder and dh/dt is rate of vertical displacement of piston with respect to time , i.e, (dh/dt) is speed of piston .

From eqn.(3) and (4) , we get speed of piston as

Speed of piston = 4 cm/s

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