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(D) For an ideal gas,the internal energy depends only on temperature. Since the temperature of the gas remains unchanged,the change in internal energy

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$\frac{i^2 R}{mg}$

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(D) For an ideal gas,the internal energy depends only on temperature. Since the temperature of the gas remains unchanged,the change in internal energy $\Delta U = 0$.According to the first law of thermodynamics,$\Delta Q = \Delta U + W$. Since $\Delta U = 0$,we have $\Delta Q = W$.The heat supplied by the resistance coil in time $t$ is $\Delta Q = i^2 R t$.The work done by the gas in moving the piston of mass $m$ upward by a distance $x$ is $W = mgx$ (since atmospheric pressure is neglected).Equating the two,we get $i^2 R t = mgx$.Differentiating with respect to time $t$,we get $i^2 R = mg \frac{dx}{dt}$.Since the speed of the piston is $v = \frac{dx}{dt}$,we have $i^2 R = mgv$.Therefore,the speed of the piston is $v = \frac{i^2 R}{mg}$.

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