🌋 Geothermal Resources & Earth Structure
"Geothermal energy is the thermal energy generated and stored in the Earth. It originates from radioactive decay and primordial heat from planet formation. Geothermal gradient: 25–30°C/km."
Temperature Gradient Formula:
$$ T_d = T_{surface} + G_{geo} \times d \quad (G \approx 25\text{-}30\,°C/km) $$
Hydrothermal
Steam/liquid, <250°C
Geopressured
High-P brine, methane
Petrothermal
Hot dry rock (HDR)
🌡️ Depth Temperature Calculator
At 3 km: T ≈ 115°C
⚙️ Geothermal Power Plant & Efficiency
Carnot Efficiency ($\eta$):
$$ \eta_{\text{max}} = 1 - \frac{T_L}{T_H} $$
Real geothermal efficiency: 7–10% (much lower due to low source temperature)
📊 Carnot Efficiency Calculator
η ≈ 33.8%
⚡ Magneto-Hydrodynamics (MHD) Principles
Lorentz Force & Induced EMF ($E$):
$$ \vec{F} = q(\vec{v} \times \vec{B}) \quad \rightarrow \quad E = B v d $$
2000V
🛰️ MHD Combined Cycle & Applications
Combined Cycle Efficiency:
$$ \eta_{combined} = \eta_{MHD} + (1-\eta_{MHD})\cdot\eta_{steam} $$
$$ \eta_{combined} \approx 58\% \quad \text{vs } 40\% \text{ (steam alone)} $$
Steam Only
η ≈ 40%
MHD Only
η ≈ 30%
Combined
η ≈ 58%
🌍 Geothermal: India Potential & Global
🧠 Module 10 Master Quiz
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