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Heat Engines

Objectives

  • What a heat engine is

The first law of thermodynamics states that energy can be converted from one form to another but cannot be created or destroyed. The first law is a conservation law, a simple accounting principle that tells us how a system's “energy ledger” is kept in balance. Although the first law tells us what forms of energy are involved in a particular energy conversion, it tells us nothing about whether the conversion is possible or in which direction the conversion process occurs. For example, consider the system in Figure 22. A closed tank containing a fluid has a shaft that facilitates the transfer of work to the fluid. When the shaft rotates, work is transferred to the fluid, increasing its internal energy thereby transferring heat from the fluid to the surroundings, as shown in Figure 22a. During this process, work is converted directly and completely to heat. But when heat is transferred to the fluid, as shown in Figure 22b, the shaft does not rotate, and thus no work is performed. The first law of thermodynamics does not preclude the conversion of heat to work in this system, but we know from experience that this conversion does not occur. Based on this argument, we conclude that work can be converted to heat directly and completely, but heat cannot always be converted to work. The direct conversion from heat to work is impossible without the use of a special device called a heat engine.


. Work can always be converted to heat (a), but heat cannot always be converted to work (b).

A heat engine is a device that converts heat to work. Before describing how this conversion occurs, we must define an important thermodynamic term, thermal energy reservoir. A thermal energy reservoir is a body with a very large thermal capacity. The distinctive characteristic of a thermal energy reservoir is that it can supply or receive large amounts of thermal energy without experiencing any change in temperature. In actual thermodynamic systems, expansive bodies of water such as oceans, lakes or rivers are considered thermal energy reservoirs because of their large masses and high heat capacities. The atmosphere is also considered a thermal energy reservoir. Any region or body whose thermal capacity is large compared to the amount of heat it supplies or receives may be considered a thermal energy reservoir. There are two types of thermal energy reservoirs, a thermal energy source and a thermal energy sink. A thermal energy source supplies heat to a system, whereas a thermal energy sink absorbs heat from a system. As illustrated in Figure 23, a heat engine receives an amount of heat, Qin, from a high-temperature source and converts a portion of that heat to work, Wout. The heat engines rejects the remaining heat, Qout, to a low-temperature sink. There are several thermodynamic systems that qualify as heat engines, but the system that best fits the definition of a heat engine is the steam power plant. In a steam power plant, Qin is the heat supplied to a boiler from a combustion process or nuclear reaction. The heat, Qout, rejected to a low temperature sink is the heat transferred from a heat exchanger to a nearby lake, river, or the atmosphere. The work, Wout, produced by the power plant is the energy generated by a turbine. An electrical generator, which is connected to the turbine via a shaft, generates electrical energy.


. A heat engine converts a portion of the heat it receives from a high-temperature source to work and rejects the remaining heat to a low-temperature sink.

By inspection of Figure 23, the first law of thermodynamics for a heat engine is

 


The work, Wout, is the useful work produced by the heat engine. For a steam power plant, Wout is actually a net work because some work has to be supplied to a pump in order to circulate the steam through the boiler and other power plant components. The heat, Qout, rejected to a low-temperature sink is wasted energy. So why don't we just eliminate Qout, converting all Qin to work? It turns out that, while this idea sounds very attractive, the elimination of Qout violates the second law of thermodynamics. A nonzero amount of waste heat, Qout, is necessary if the heat engine is to operate at all.

Efficiency is a useful engineering quantity that is used to measure the performance of numerous engineering systems. A general definition of efficiency is

 


For heat engines, the desired output is the work output, and the required input is the heat supplied by the high temperature source. Hence, thermal efficiency of a heat engine, denoted th, is given by the relation

 


In accordance with the first law of thermodynamics, no heat engine (or any other device for that matter) can produce more energy than is supplied to it. Therefore, the thermal efficiency of a heat engine is always less than 1. This fact is apparent from Figure 23 because only a portion of the heat supplied to the heat engine is converted to work, the remaining heat being rejected to a low-temperature sink.

EXAMPLE

A heat engine produces 6 MW of power while absorbing 10 MW from a high-temperature source. What is the thermal efficiency of this heat engine? What is the rate of heat transfer to the low-temperature sink?

 

Solution

The work output and heat input are given in terms of energy rates, not energy. The first law relation for a heat engine, Equation 6-34, may be expressed in rate form by dividing each quantity by time. Similarly, the work and heat quantities in Equation 6-36 may be divided by time. Dividing the work and heat quantities by time yields power, , and heat transfer rates, and , where the “dot” denotes a rate quantity. Thus, the thermal efficiency of the heat engine is

The rate of heat transfer to the low-temperature sink is


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