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

"13.48 Kwhr" is the right solution.

Step-by-step 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=(\pi)/(4) d^2`

On substituting the values, we get

⇒
`=(3.14)/(4) (8)^2`

⇒
`=0.785* 64`

⇒
`=50.24 \ m^2`

Total heat generation rate will be:

⇒
`Q=q* A`

`=0.063* 50.24`

`=3.16 \ W`

hence,

The electricity generation capacity will be:

⇒
`P=\eta Q t`

On substituting the values, we get

⇒
`=0.5* 3.16* 8760`

⇒
`=13840.8 \ Whr`

On converting into Kwhr, we get

⇒
`=13.84 \ Kwhr`