Problem — Power output of a coal power plant

Problem

Estimate the net electrical power of a thermoelectric power plant burning $10\;\text{kg/s}$ of coal ($q \approx 25\;\text{MJ/kg}$), with an overall efficiency of $40\%$.

Solution

Input thermal power. The coal burned per second releases a thermal power equal to mass flow rate $\times$ calorific value:

$P_\text{in} = \dot{m}\, q = 10\;\text{kg/s} \times 25\;\text{MJ/kg} = 250\;\text{MW}$

Electrical power. Only the fraction $\eta$ of this power becomes usable electricity:

$P_\text{el} = \eta\, P_\text{in} = 0{,}40 \times 250\;\text{MW} = \ev{100\;\text{MW}}$

A $100\;\text{MW}$ plant is medium-sized. The calculation also shows the flip side: $150\;\text{MW}$ (the $60\%$) is discharged as heat into the environment — into rivers, the sea, or cooling towers. The Carnot limit between the steam temperature ($\sim 800\;\text{K}$) and the surroundings ($\sim 300\;\text{K}$) would give $\sim 60\%$; the real $40\%$ is consistent with practical losses.

Collegamenti

Argomenti: Macchine termiche Concetti: Rendimento Competenze: Stime di Fermi Oggetti: Macchina termica