Physics - Heat & Thermo Question with Solution | TestHub

$\text{P}=1000\text{ watt}$

$\therefore {\text{P}}_{\text{in}}=\left(1000-160\right) \text{J/s}=840\text{ J/s}$

Now,$\frac{\text{d}\text{Q}}{\text{dt}}=\text{ms}\frac{\text{dT}}{\text{dt}}$

$\therefore 840=\text{ms}\frac{\text{dT}}{\text{dt}}$

$\therefore \text{dt}=\frac{\text{ms}}{840}\text{dT}$

Integrating both sides we have;

$\text{t}=\frac{\text{ms}}{840}\int \text{dT}$

$=\frac{\left(2\times 1000\times 10^{-6}\times 1000\right)\times \text{4.2}\times 1000}{840}\times 50$

$=500sec$

$=\mathrm{8 }min20sec$