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 $L=80cal{g}^{-1}$)

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

Answer 1

The correct option is A $2.04cal$

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 0 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 10 g of ice is

$Q_2=mL=10\times 80=800cal$

According to given problem $Q_1=Q_2$

$\therefore 392.5s=800$ or $s=2.04cal{cm}^{-2}{min}^{-1}$