A source supplies heat to a system at the rate of 1000 W . If the system performs work at a rate of 200 W . The rate at which internal energy of the system increases is

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According to the first law of thermodynamics, $Q = W + U$ .
Upon differentiation, we get
$\frac{d Q}{d t} = \frac{d W}{d t} + \frac{d U}{d t} \Rightarrow \frac{d U}{d t} = \frac{d Q}{d t} - \frac{d W}{d t}$
Given: $\frac{d Q}{d t} = 1000 W$
$\frac{d W}{d t} = 200 W$
Therefore, $\frac{d U}{d t} = 1000 W - 200 W = 800 W$

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