## Supplementary exercises

Some topics of science and technology make use of numerical information and formulas. It will deepen your understanding of principles if you are comfortable with these numbers and at least be able to read documents using the numbers and appreciate their significance.The exercises below, mainly calculations, support the material in the following Resource Sections of the book

### Resource 2 Principles of Heat

**Questions**

- (a) Convert the following temperatures from degrees Celsius to degrees kelvin: 20°C; 400°C; –10°C.

(b) Convert the following temperatures from degrees kelvin to degrees Celsius: 200 K; 300 K; 773 K. - Explain, using accurate terminology, the reasons for the following observations.

(a) The meat and gravy inside a hot pie burn the tongue more easily than the surrounding pastry, even though all parts of the pie are at the same temperature.

(b) A concrete floor feels colder to walk on than carpet, even though both are at the same temperature. - Calculate the total heat required to convert 2 kg of water at 60°C completely to steam at 100°C. (Given: the specific heat capacity of water is 4200 J/kg K and the specific latent heat of steam is 2260 kJ/kg.)
- An insulated hot-water storage cylinder has internal dimensions of 0.6 m dia. and 1.5 m height. A heating element at the bottom of the cylinder supplies 74.81 MJ of heat to the water which is at an initial temperature of 8°C. Ignore any heat losses from the water and heat gains by the cylinder itself.

(a) Calculate the mass of water present in the cylinder.

(b) Calculate the temperature of the water after heating.

(c) Calculate the effective power of the heating element if the above temperature rise takes 4 hours.

Given: density of water = 1000 kg/m3; specific heat capacity of water = 4200 J/kg K. - Explain, with accurate reference to appropriate mechanisms of heat transfer, the following effects.

(a) The ability of a vacuum flask to keep liquids either hot or cold.

(b) The ability of silver paint on a roof to reduce heat loss from a building. - At standard temperature and pressure a certain sample of gas occupies 50 litres in volume. Calculate the pressure required to compress this sample to a volume of 20 litres while allowing the temperature to rise to 30°C.

### Resource 4 Principles of Electricity

**Questions**

- The potential difference across a certain resistor in a television circuit is found to be 450 V when a current of 150 mA is flowing through the resistor. Calculate the value of this resistor.
- Draw the circuit diagram of a 3 W and a 4 W resistor connected in series together, with a potential difference of 14 V applied across them.

(a) Calculate the total current flowing in the circuit.

(b) Calculate the voltage drop across the 3 W resistor. - Draw the circuit diagram of a 5 W and a 20 W resistor connected together in parallel, with a potential difference of 80 V applied across them.

(a) Calculate the total resistance of the circuit.

(b) Calculate the total current flowing in the circuit.

(c) Calculate the current flowing in the 5 W resistor. - A 20 m length of cable carries a continuous current of 10 A. At this current the cable has a resistance of 4 m W /m.

(a) Calculate the total power loss in this cable.

(b) Calculate the total energy lost in the cable during 24 hours. - Calculate the current that flows in a 60 W light bulb when it is connected to a 230 V supply. How many such bulbs, wired in parallel, could be safely connected to an outlet which is fitted with a 3 amp fuse?
- A 136 litre hot-water storage cylinder is heated by a 230 V electric element that has a resistance of 15 W . Assume that no energy is lost in the heating process.

(a) Calculate the power rating of the element.

(b) Calculate the energy needed to raise the temperature of the entire contents from 5°C to 60°C.

(c) Calculate the time taken to raise the temperature as above.

Given: density of water is 1000 kg/m3 and specific heat capacity of water is 4200 J/kg °C. - A transformer with 200 turns in the primary winding is to step-up voltage from 12 V to 230 V. Assume that the transformer is 100% efficient.

(a) Calculate the number of turns needed in the secondary winding.

(b) Calculate the current flowing in the primary winding when a 100 W lamp is connected to the output. - The apparent power rating of an AC motor is 4000 VA and it has a power factor of 0.85.

(a) Calculate the output power of the motor.

(b) Calculate the current drawn from the 230 V mains.

(c) Calculate the peak value of this current.

### Resource 5 Principles of Water Technology

**Questions**

- When an oil-filled manometer measures a certain pressure the difference in oil levels is 240 mm. Express this pressure as an absolute pressure. Given: density of the oil is 830 kg/m3; gravitational acceleration is 9.81 m/s2.
- A reservoir dam, 200 m in length, has a vertical face which retains water to a depth of 15 m. Calculate the horizontal force on the dam produced by the retained water. Given: density of water is 1000 kg/m3; gravitational acceleration is 9.81 m/s2.
- A 200 mm diameter pipe runs into a 150 mm diameter pipe with a discharge rate of 0.04 m3/s. If both pipes are running full bore then calculate the flow velocities in each pipe.
- A venturimeter has a throat of 80 mm diameter and is set in a horizontal water main of 150 mm diameter. If the measured pressure heads are 13.7 m in the main and 10.5 m in the throat then calculate the flow rate in the pipe. Given: discharge coefficient for the meter is 0.98; gravitational acceleration is 9.81 m/s2.
- A 100 mm diameter water main is required to discharge at 0.035 m3/s when running full bore. Calculate the loss of pressure head that occurs in a 150 m horizontal run of this pipe. Use Darcy’s formula and assume a friction coefficient of 0.006 for the pipe.
- A circular drain of 150 mm diameter is laid with a fall of 1 in 40 and is running half-full of water. Assume a Chézy coefficient is 50 m1/2/s.

(a) Calculate the flow velocity in the drain.

(b) Calculate the discharge rate (in m3/s) for these conditions.