Question

Rays from the sun are focused by a lens of diameter $5cm$ on to a block of ice and $10g$ of ice is melted in $20min$. Therefore the heat from the sun reaching the earth per $min$ per square centimetre is
(Latent heat of ice $L=80cal{g}^{-1}$)

• A. $2.04cal$
• B. $0.51cal$
• C. $4.08cal$
• D. $3.02cal$

Answer 1

Answer: (A)

If $s$ calorie of heat is received from the sun per $c{m}^2$ per minute, the heat collected by the lens of radius $2.5cm$ in $20$ minutes is
$Q_1=s\times A\times t=s\times \pi \times {\left(2.5\right)}^2\times \left(20\right)$
$=\left(392.5\right)scal$
Heat required to melt $10g$ of ice is
$Q_2=mL=10\times 80=800cal$
According to given problem $Q_1=Q_2$
$\therefore 392.5s=800$ or $s=2.04calc{m}^{-2}mi{n}^{-1}$