A source supplies heat to a system at the rate of 1000W . If the...

According to the first law of thermodynamics, $Q = W + U$.

Upon differentiation, we get

$\dfrac{dQ}{dt} = \dfrac{dW}{dt} + \dfrac{dU}{dt} ⇒ \dfrac{dU}{dt} = \dfrac{dQ}{dt} - \dfrac{dW}{dt}$

Given: $\dfrac{dQ}{dt} = 1000W$

$\dfrac{dW}{dt} = 200W$

Therefore, $\dfrac{dU}{dt} = 1000W - 200W = 800W$