Daily Work Done by a Coal-Fired Power Station, Its Efficiency and Carbon Dioxide Emissions

We can use $W=Q_{\text{h}}-Q_{\text{c}}$ to find the work output $W$, assuming a cyclical process is used in the power station. In this process, water is boiled under pressure to form high-temperature steam, which is used to run steam turbine-generators, and then condensed back to water to start the cycle again.

Work output is given by:

Substituting the given values:

The efficiency can be calculated with $\text{Eff}=\frac{W}{Q_{\text{h}}}$ since $Q_{\text{h}}$ is given and work $W$ was found in the first part of this example.

Efficiency is given by: $\text{Eff}=\frac{W}{Q_{\text{h}}}$. The work $W$ was just found to be ${\text{1.02 × 10}}^{\text{14}}\text{J}$, and $Q_{\text{h}}$ is given, so the efficiency is

The daily consumption of coal is calculated using the information that each day there is $2\text{.}\text{50}\times {\text{10}}^{\text{14}}\text{J}$ of heat transfer from coal. In the combustion process, we have _{$\text{C}+{\text{O}}_2\to {\text{CO}}_2$}. So every 12 kg of coal puts 12 kg + 16 kg + 16 kg = 44 kg of _{${\text{CO}}_2$} into the atmosphere.

The daily coal consumption is

Assuming that the coal is pure and that all the coal goes toward producing carbon dioxide, the carbon dioxide produced per day is

This is 370,000 metric tons of _{${\text{CO}}_2$} produced every day.

If all the work output is converted to electricity in a period of one day, the average power output is 1180 MW (this is left to you as an end-of-chapter problem). This value is about the size of a large-scale conventional power plant. The efficiency found is acceptably close to the value of 42% given for coal power stations. It means that fully 59.2% of the energy is heat transfer to the environment, which usually results in warming lakes, rivers, or the ocean near the power station, and is implicated in a warming planet generally. While the laws of thermodynamics limit the efficiency of such plants—including plants fired by nuclear fuel, oil, and natural gas—the heat transfer to the environment could be, and sometimes is, used for heating homes or for industrial processes. The generally low cost of energy has not made it economical to make better use of the waste heat transfer from most heat engines. Coal-fired power plants produce the greatest amount of _{${\text{CO}}_2$} per unit energy output (compared to natural gas or oil), making coal the least efficient fossil fuel.