Question

You are hired to build a geothermal power plant that absorbs heat from a hot water spring and discards heat into the surrounding air, which is at a temperature of 28°. The plant is designed for a maximum (Carnot) efficiency of 0.15.

What is the temperature, in degrees Celsius, of the hot water gushing from the spring?

Answer 1

Temperature of the hot water from the spring = T_h

Temperature of the surrounding air = T_c = 28 ^oC = 28 + 273 K = 301 K

Carnot efficiency of the plant = $\eta$ = 0.15

$\eta = 1 - \frac{T_{c}}{T_{h}}$

$0.15 = 1 - \frac{301}{T_{h}}$

$\frac{301}{T_{h}} = 0.85$

T_h = 354.12 K

Converting to degrees Celsius,

T_h = 354.12 - 273

T_h = 81.12 ^oC

Temperature of the hot water gushing from the spring = 81.12 ^oC