Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators

"One of the most important things we can do with heat is to use it to do work for us. A **heat engine** does exactly this—it makes use of the properties of thermodynamics to transform heat into work." "A **cyclical process** brings a system, such as the gas in a cylinder, back to its original state at the end of every cycle. All heat engines use cyclical processes." "Because there is no change in internal energy for a complete cycle ($\Delta U = 0$), we have $0 = Q - W$, so that $W = Q.$ … $W = Q_h - Q_c$ for a cyclical process." "According to the second law of thermodynamics, heat engines cannot have perfect conversion of heat into work. … there is a minimum amount of $Q_h$ that cannot be used for work." "**Heat pumps**, air conditioners, and refrigerators utilize heat transfer of energy from low to high temperatures, which is the opposite of what heat engines do. … the total heat transfer to the hot reservoir is $Q_h = Q_c + W.$" "We define thermal efficiency, *Eff*, to be the ratio of useful energy output to the energy input … $Eff = \frac{W}{Q_h}.$ An efficiency of 1, or 100 percent, would be possible only if there were no heat to the environment ($Q_c = 0$)." "All values of heat ($Q_h$ and $Q_c$) are positive; there is no such thing as negative heat. The *direction* of heat is indicated by a plus or minus sign." "(a) What is the work done by the power station? … $W = 2.50 \times 10^{14}\text{ J} - 1.48 \times 10^{14}\text{ J} = 1.02 \times 10^{14}\text{ J}.$ (b) … $Eff = \frac{1.02 \times 10^{14}\text{ J}}{2.50 \times 10^{14}\text{ J}} = 0.408,\text{ or } 40.8\%.$"