# TEMPERATURE, WORK AND HEAT

The temperature scale now in general use is the Celsius scale, based nominally on the melting point of ice at 0°C and the boiling point of water at atmospheric pressure at 100°C (by strict definition, the triple point of ice is 0.01°C at a pres­sure of 6.1 mbar).

The law of conservation of energy tells us that when work and heat energy are exchanged there is no net gain or loss of energy. However, the amount of heat energy that can be converted into work is limited. As the heat flows from hot to cold a certain amount of energy may be converted into work and extracted. It can be used to drive a generator, for example.

The minimum amount of work to drive a refrigerator can be defined in terms of the absolute temperature scale. Figure 1.1 shows a reversible engine E driving a reversible heat pump P; Q and W represent the flow of heat and work. They are called reversible machines because they have the highest efficiency that can be visualised, and because there are no losses, E and P are identical machines.

The arrangement shown results in zero external effect because the reser­voirs experience no net gain or loss of heat. If the efficiency of P were to be higher, i. e. if the work input required for P to lift an identical quantity of heat Q2 from the cold reservoir were to be less than W, the remaining part of W could power another heat pump. This could lift an additional amount of heat.

The result would be a net flow of heat from the low temperature to the high 1 Figure 1.1 Ideal heat engine, E, driving an ideal refrigerator (heat pump), P

Temperature without any external work input, which is impossible. The rela­tionship between Q1, Q2 and W depends only on the temperatures of the hot and cold reservoirs. The French physicist Sadi Carnot (1796-1832) was the first to predict that the relationship between work and heat is temperature — dependent, and the ideal refrigeration process is known as the Carnot cycle. In order to find this relationship, temperature must be defined in a more funda­mental way. The degrees on the thermometer are only an arbitrary scale.

Kelvin (1824-1907), together with other leading physicists of the period, concluded that an absolute temperature scale can be defined in terms of the efficiency of reversible engines. Figure 1.2 William Thomson, appointed to the chair of natural philosophy at Glasgow University, aged 22, published his paper on the absolute temperature scale two years later. He became Lord Kelvin in 1892 (Glasgow University)

The ideal ‘never-attainable-in-practice’ ratio of work output to heat input (W/Qj) of the reversible engine E equals: Temperature Difference (T1 — T0) divided by the Hot Reservoir Temperature (Tj).

In Figure 1.1 the device P can be any refrigeration device we care to invent, and the work of Kelvin tells us that the minimum work, W necessary to lift a quantity of heat Q2 from temperature T0 to temperature T1 is given by:

W = Q2 (T — T0)

To

The temperatures must be measured on an absolute scale i. e. one that starts at absolute zero. The Kelvin scale has the same degree intervals as the Celsius scale, so that ice melts at +273.16K, and water at atmospheric pressure boils at +373.15K. On the Celsius scale, absolute zero is -273.15°C. Refrigeration ‘ efficiency’ is usually defined as the heat extracted divided by the work input. This is called COP, coefficient of performance. The ideal or Carnot COP takes its name from Sadi Carnot and is given by:

COP = = —To——-

W (T — To)

Example 1. 1

Heat is to be removed at a temperature of -5°C and rejected at a temperature of 35°C. What is the Carnot or Ideal COP?

Convert the temperatures to absolute:

-5°C becomes 268 K and 35°C becomes 308 K (to the nearest K)

268

 6.7 Carnot COP

(308 — 268)

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