Subsection 3.3.2 Transforming Heat to Work
The energy transformation of primary interest in the shipboard steam plant is the transformation from heat to work. To see how this transformation occurs, we need to consider the pressure, temperature, and volume relationships which hold true for gases. These relationships may be summarized as follows:
- When the temperature is held constant, increasing the pressure on a gas causes a proportional decrease in volume. Decreasing the pressure causes a proportional increase in volume.
- When the pressure is held constant, increasing the temperature of a gas causes a proportional increase in volume. Decreasing the temperature causes a proportional decrease in volume.
- When the volume is held constant, increasing the temperature of a gas causes a proportional increase in pressure. Decreasing the temperature causes a proportional decrease in pressure.
Suppose we have a boiler in which steam has just begun to form. With the steam stop valves still closed, the volume of the steam remains constant while the temperature and the pressure are both increasing. When operating pressure is reached and the steam stop valves are opened, the high pressure of the steam causes the steam to flow to the turbines. The pressure of the steam thus provides the potential for doing work; the actual conversion of heat to work is done in the steam turbines. The change in the internal energy (as indicated by changes in pressure and temperature) of the steam between the boiler and the condenser is an indication of the amount of heat that has been converted to work in the turbines.
Since heat is measured in BTU and work is measured in foot-pounds, how can we compare the amount of energy put in as heat with the amount of energy put out as work? At first glance, asking how much heat equals how much work might seem like asking how many lima beans equals playing baseball. However, the problem is not that difficult, since both heat and work are forms of energy. The formula for converting heat to work is
\begin{equation*}
1 \text{ BTU} = 778 \text{ ft-lb}
\end{equation*}
or, in other words, the amount of energy required to raise the temperature of 1 pound of water 1 °F is the same as the amount of energy required to lift a 1-pound weight 778 feet against the force of gravity.
