An ideal gas is kept in a closed, rigid and heat insulating vessel. A coil of resistance 100 ohm, carrying a current of 1 ampere, is supplying heat to the gas for 5 minutes. What will be the change of internal energy of the gas?

Explanation

Since the vessel in insulated , exchange of heat Q = 0
Work done by electrical energy in 5 minutes, i.e., 300 seconds,
`W = I^(2)Rt = I^(2) xx 100 xx 300 = 30000 J`
This work is supplied to the gas from outside. So it is negative,
i.e., W = - 30000J.
From the first law of thermodynamics,
`Q = (U_(f) - U_(i)) + W`
or, `0 = Delta U + (-30000)`
`[Delta U = U_(f) - U_(i)` = change of internal energy] or, `Delta U = 30000J`.