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

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

Options

A1200 W
B600 W
C500 W
D800 W

Correct answer

D. 800 W

Step-by-step solution

Given, Rate of heat supplied,

\frac{\mathrm{dQ}}{\mathrm{dt}}=1000 \mathrm{ W}

Rate of work performed,

\frac{\mathrm{dw}}{\mathrm{dt}}=200 \mathrm{ W}

Using first law of thermodynamics

d Q=d U+d w (\Rightarrow \frac{\mathrm{dU}}{\mathrm{dt}}=\frac{\mathrm{dQ}}{\mathrm{dt}}-\frac{\mathrm{dw}}{\mathrm{dt}} \Rightarrow \frac{\mathrm{dU}}{\mathrm{dt}}=1000-200=800)

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