UCCS PES/ENSC 2500 Renewable Energy
Chapter 15 Geothermal Energy
name: _________________________
Problem 15.1
Calculate the ideal Carnot efficiency for a turbine operating with a hot reservoir at a temperature of
440°F and a cold reservoir at a temperature of 170°F.
Converting temperatures to absolute degrees (Kelvin) gives
Then the Carnot efficiency is
Problem 15.4
Heat is extracted from hot rock at a temperature of 250°C and used to produce electricity with the ideal
Carnot efficiency.
If the temperature of the cold reservoir is 75°C, what mass of rock would be needed to yield 1 GWhe.
See Chapter 8 for the thermal properties of typical rock, and assume a generator efficiency of 90%.
The heat extracted from rock is
Q = CmΔT.
From Table 8.6, for rock C = 879 J/(kg ºC).
We need a net energy of 1 GWhe and at 90% efficiency the total energy required is (1 GWhe)/(0.9) = 1.1 GWh.
Converting this to Joules gives
For the temperatures given for the hot and cold reservoirs in ºC, we calculate the equivalent temperatures in K as
Thus the ideal Carnot efficiency is η =
This means that the total energy required is
For ΔT = _________________________________ the mass is
Problem 15.6
Assume that geothermal heat transfer (at least near the surface of the earth) is by conduction through the
crust rocks.
2
For an average geothermal heat flow of 0.087 W/m and typical thermal gradient of 100°C/km, calculate the
thermal conductivity of the rock.
Compare with the known thermal conductivities of similar materials given in Chapter 8.
Equation (8.4) gives
where k is the thermal conductivity, A is the area, ΔT is the temperature difference and l is the distance.
Solving for k gives
So in this case P/A = 0.087 W/m and ΔT/l = 100ºC/km or 0.001ºC/cm.
2
The thermal conductivity is then
From Table 8.1,
The values for concrete and brick are: 170
value for rock is in the proper range.
and 71
respectively, so the calculated