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Most materials increase slightly in dimension when their temperature increases. For instance, overhead lines sag more in the summer than in the winter, and a long straight conduit run may buckle in very hot weather if expansion bends are not fitted. Similarly, dimensions often decrease when temperature decreases. An overhead cable that is erected in hot weather and strained tightly will contract in cold weather; the extra stress may then result in stretching or even breaking.

Although expansion with increasing temperature is often a nuisance, it can be applied with advantage when used to control temperature. Some metals expand more than others when heated through the same temperature range. If two strips, one of each of two metals with different rates of expansion, are riveted together, the bimetal

strip so formed will bend when heated. If a set of contacts is operated by the strip as

it bends, the device can be made to control temperature and is called a thermometer. Another type of thermostat based on the same principle is called a rod-type thermostat. A rod of material, selected for its small increase in length when heated, is mounted

Heat 87 within a tube of brass, the rod and the tube being welded together at one end. Changes in the temperature of the device result in differing changes in length of the rod and the tube, thus operating a switch. The slow break resulting from the slow rate of differential expansion will give rise to arcing at the contacts of a directly operated switch. Permanent-magnet systems and flexed springs are often used to give a quick make-and-break action to the switch (Figures 4.1 and 4.2).

temperature- setting knob flexible member bimetal back stop armature magnet moving contact fixed contact terminals

Figure 4.1 Air thermostat

temperature- setting knob back stop switch member nonexpanding rod expanding tube fixed contact moving contact armature magnet

4.7 Summary of formulas for Chapter 4

temperature in kelvin = temperature in degrees Celsius +273 temperature in degrees Celsius = temperature in kelvin −273 heat energy for temperature change, J = mass, kg × temperature change, K

× specific heat, J/kg K energy, J = power, W × time, s

4.8 Exercises

1 Express the following temperature in kelvin: (a) 60◦_{C (b) −75}◦_{C (c) 1000}◦_C

2 Express the following temperatures in degrees Celsius: (a) 320 K (b) 1500 K (c) 240 K

3 A small storage heater contains 8 litres of water at a temperature of 10◦_{C. How}

much heat energy must be provided to raise the water temperature to 90◦_{C? The}

specific heat of water is 4187 J/kg K.

4 How much heat energy must be supplied to 20 kg of brass to increase its temper- ature by 500 K? Give your answer in joules and in kilowatt hours. The specific heat of brass is 376 J/kg K.

5 A hall measures 10 m by 30 m, by 5 m high. How much heat energy will be required to raise the temperature of the air it contains from 5◦_{C to 22}◦_{C? 1 m}3

of air has a mass of 1.26 kg. The specific heat of air is 1010 J/kg K. Express your answer in kilowatt hours.

6 Calculate the amount of heat in joules required to raise the temperature of 100 g of aluminium from 10◦_{C to 710} ◦_{C. The specific heat of aluminium is 915}

J/kg K.

7 Forty litres of water is heated from 8◦_{C to 78}◦_{C, the efficiency of the oper-}

ation being 70%. How much heat is required? The specific heat of water is 4187 J/kg K.

8 The rate of flow of water through a water-cooled motor is 0.2 litres/s, and inlet and outlet temperatures are 10◦_{C and 20}◦_{C, respectively. At what rate is heat}

being removed from the motor? The specific heat of water is 4187 J/kg K. 9 An electric-arc furnace is used to raise the temperature of 4000 kg of iron from

12◦_{C to 812}◦_{C, the overall efficiency of the furnace being 40%. What energy}

input in kilowatt hours is required? The specific heat of iron is 497 J/kg K. 10 An electric water heater is 80% efficient and consumes energy at the rate of

2000 J/s. If the heater initially contains 10 litres of water at 12 ◦_{C, what}

will be the temperature after 10 min of heating? The specific heat of water is 4187 J/kg K.

11 The input power to a furnace for heating copper is 10 kW, and the furnace is 39.7% efficient. By how much will the temperature of 150 kg of copper have increased after 30 min? The specific heat of copper is 397 J/kg J.

Heat 89 12 A 2 kW heater is switched on in a room 5 m square and 3 m high, when the air temperature is 70◦_{C. If 70% of the heat provided is lost, what will be the air}

temperature after 20 min? 1 m3_{of air has a mass of 1.26 kg, and the specific heat}

of air is 1010 J/kg K.

13 How long will it take a 1.5 kW heater to raise the temperature of 10 litres of water by 60◦_{C if the heater is 100% efficient? The specific heat of water is 4187 J/kg K.}

14 An instantaneous-type water heater is required to provide a continuous flow of water of 2 litres/min at a temperature of 85◦_{C with an inlet water temperature of}

10◦_{C. What must be the electrical loading in kilowatts if the heater is assumed}

to be 100% efficient? The specific heat of water is 4187 J/kg K.

15 A furnace for lead casting contains 120 kg of lead, and is heated by a 6 kW element. The initial temperature of the lead is 20◦_{C. What temperature will the}

lead reach after 1 h if the furnace is 25% efficient? The specific heat of lead is 129 J/kg K.

4.9 Multiple-choice exercises