Question

Earth receives $1400W/m^2$ of solar power. If all the solar energy falling on a lens or area $0.2m^2$ is focused on to a block of ice of mass $280g$, the time taken to melt the ice will be _______ minutes (latent heat of fusion of ice $=3.3\times {10}^{5}J/kg)$.

Answer 1

Solar power received by earth $=1400W/m^2$
Solar power received by $0.2m^{2}area=\left(1400W/m^2\right)\left(0.2m^2\right)=280W$
Mass of ice $=280g=0.280kg$
Heat required to melt ice
$=\left(0.280\right)(3.3\times {10}^5)$
$=9.24\times {10}^{4}J$
If $t$ is the time taken for the ice to melt, we will have
$\left(280\right)t=9.24\times {10}^{4}J[\therefore P=\frac{E}{t}]$
$t=\frac{9.24\times {10}^4}{280}s=330s=5.5min$.