Physics Topics such as mechanics, thermodynamics, and electromagnetism are fundamental to many other scientific fields.
What is Meant by Heat Reservoir? What is an Ideal Heat Engine?
Heat reservoir: A body whose temperature remains constant even when heat is gained or lost by it is called a heat reservoir. Every heat reservoir has its own characteristic temperature. Generally different heat reservoirs have different characteristic temperatures. They are drawn in the way as shown in Fig.
The characteristic temperatures of the two reservoirs shown in Fig.(a) and (b) are T1 and T2 respectively.
For example, atmosphere or sea water may be taken as heat reservoir. If a burning oven is placed in air, it rejects heat to the atmosphere. Or if a large block of ice is placed in air, it receives heat from the atmosphere. From our daily experiences it is known that we can ignore the change of temperature of the atmosphere in the above cases. Similarly if a bucketful of boiling water is poured in sea, sea water takes heat but its temperature does not change.
It is obvious that atmosphere and sea, being very large in size, behave as heat reservoirs. However, comparatively smaller bodies also may show similar properties. Suppose, the temperature of a coal-oven when burning is 300°C. It continuously rejects heat to the surroundings. In spite of that, as long as coal burns, the temperature of the oven remains constant at 300°C. So in this case the oven acts as a heat reservoir.
We know, if dT is the change of temperature of a body due to a heat exchange of dQ, then the thermal capacity of the body, C = \(\frac{d Q}{d T}\). In case of a heat reservoir, dT = 0; so whatever the value of heat gain or heat loss (dQ) may be, C → ∞, i.e., the thermal capacity of any heat reservoir is infinite. Conversely it can be said that if the thermal capacity of a body is infinite, the body will behave as a heat reservoir.
Heat engine: It is a mechanical device which converts heat into work.
In general, a heat engine H [Fig.] takes heat from a source at higher temperature, converts a part ot it into work and gives out the rest to a body (sink) at lower temperature.
In most cases, the source at a higher temperature and the sink at a lower temperature are two heat reservoirs, i.e., in a complete cycle their temperatures are fixed at T1 and T2 [Fig.]. Obviously, T1 > T2.
Generally, a heat engine works in a cyclic process. It means that, after completion of a cycle by converting heat into work, the working substance of the engine returns to its initial condition and becomes ready for the next cycle. Action of each cycle is equivalent, i.e., in each cycle the same amount of heat is converted into the same amount of work.
Efficiency of a heat engine: The object of a heat engine is to convert heat taken from the source into useful work. So the heat taken from the source is called the input, and the transformed work is called the output.
Efficiency of a heat engine is defined as the fraction of total heat taken from the source which is converted into work.
Suppose in each cycle,
heat taken by the engine from the source at temperature T1 = Q1 [Fig.];
transformed work = W;
heat rejected by the engine to its surroundings (sink) at temperature T2 = Q2.
From the principle of conservation of energy we can write,
Q1 = W + Q2 or, W = Q1 – Q2
So, efficiency, η \(=\frac{\text { output }}{\text { input }}\) = \(\frac{W}{Q_1}\) = \(\frac{Q_1-Q_2}{Q_1}\)
i.e., η = 1 – \(\frac{Q_2}{Q_1}\) ……… (1)
From equation (1) we get η ≤ 1, i.e., the efficiency of a heat engine can never be greater than 1 or 100%.
Ideal heat engine: It is easily understood that, the more a heat engine converts heat into work the more its efficiency will be. If any engine converts the whole amount of heat taken from the source into work [Fig.], then the engine is called an ideal heat engine.
It is evident that in case of this type of an engine, the heat rejected to its surrounding (Q2) will be zero. So the work obtained will be equal to the heat taken from the source (Q1). Therefore, the efficiency of an ideal heat engine,
η = \(\frac{W}{Q_1}\) = \(\frac{Q_1}{Q_1}\) = 1 = 100%
Alternatively, η = 1 – \(\frac{Q_2}{Q_1}\) = 1 – \(\frac{0}{Q_1}\) = 1 = 100%
Kelvin-Planck statement of the second law of thermodynamics: This statement referred to in section 1.12 is as follows.
No self-acting machine can convert some amount of heat entirely into work. On the basis of the discussion about heat engines, this statement can be expressed in the form of an easy alternative: An ideal heat engine does not exist in nature.