An electric heater supplies heat to a system at a rate of 100 W . If the system performs work at a r

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An electric heater supplies heat to a system at a rate of 100 W . If the system performs work at a rate of 75 J/s, then the rate at which internal energy increases will be:

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Sol. [Key Concept: First law of thermodynamics: ΔU = Q − W] Using $1^{	ext{st}	ext{~}}$ law of thermodynamics for electric heater,$$\begin{matrix} & Q = \Delta U + W \ & \ \Rightarrow \ \frac{dQ}{dt} = \frac{d(\Delta U)}{dt} + \frac{dW}{dt} \ & \ \Rightarrow \ 100	ext{ }W = \frac{d(\Delta U)}{dt} + 75	ext{ }W \ & \ 	herefore\ \frac{d(\Delta U)}{dt} = 25	ext{ }W \end{matrix}$$

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