Question

A solar collector for a hot water system absorbs solar radiation at the rate of 660 W/m^2
. Its collecting area is 3.8m^2 . Cold water at 15degrees enters the collector. What volume of
water per minute at an output temperature of 60 degrees can this collector deliver?

Answer 1

This question involves the concepts of the law of conservation of energy and specific heat capacity.

This collector can deliver "7.96 x 10⁻⁴ m³/min" of water at an output temperature of 60°C.

According to the law of conservation of energy:

Solar Energy = Energy Required to raise the temperature of the water

Solar Power = Energy Required to raise the temperature of the water

$IA=\frac{mC\Delta T}{t}\\\\\frac{m}{t}=\frac{IA}{C\Delta}$

where,

$\frac{m}{t}$ = mass flow rate = ?

I = solar radiation = 660 W/m²

A = Area = 3.8 m²

ΔT = change in temperature = 60°C - 15°C = 45°C

C = specific heat capacity = 4200 J/kg.°C

Therefore,

$\frac{m}{t}=\frac{(660\ W/m^2)(3.8\ m^2)}{(4200\ J/kg.^oC)(45^oC)}\\\\\frac{m}{t}=(0.0133\ kg/s)(\frac{60\ s}{1\ min})\\\\\frac{m}{t}=0.796\ kg/min$

Now, the volume flow rate will be:

$\frac{V}{t}=\frac{(\frac{m}{t})}{(density\ of\ water)}=\frac{(0.796\ kg/min)}{(1000\ kg/m^3)}\\\\\frac{V}{t}=7.96\ x\ 10^{-4}\ m^3/min$

Learn more about the law of conservation of energy here:

brainly.com/question/20971995?referrer=searchResults

The attached picture explains the law of conservation of energy.