Question

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

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

Answer 1

Answer: (A)

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