Question

Assuming the average rate of heat energy flowing outwards from earth to be 0.063 W/m2 calculate the energy available at a hot spot in Wyoming which has diameter of 8m. If the efficiency of conversion of this energy to electricity is 50% then calculate the electricity generation capacity in kWh for a period of one year. If the cost of producing 1kWh of energy is $0.12 is it worth producing electricity from this source

Answer 1

Answer:

"13.48 Kwhr" is the right solution.

Explanation:

The given values are:

Average rate of heat energy,

= 0.063 W/m²

Diameter,

= 8m

Efficiency of conversion,

= 50%

Now,

The area of hotspot will be:

⇒  $A=\frac{\pi}{4} d^2$

On substituting the values, we get

⇒      $=\frac{3.14}{4} (8)^2$

⇒      $=0.785\times 64$

⇒      $=50.24 \ m^2$

Total heat generation rate will be:

⇒  $Q=q\times A$

        $=0.063\times 50.24$

        $=3.16 \ W$

hence,

The electricity generation capacity will be:

⇒  $P=\eta Q t$

On substituting the values, we get

⇒      $=0.5\times 3.16\times 8760$

⇒      $=13840.8 \ Whr$

On converting into Kwhr, we get

⇒      $=13.84 \ Kwhr$