Exercises: Conduction, convection and radiation

A metal spoon left in a mug of hot tea in a kitchen in Galway becomes warm at the end that is not in the tea.

1. a) Name the process by which thermal energy travels along the spoon.
2. b) Using the particle model, describe how energy is passed from the hot end to the cool end of the spoon.
3. c) Explain why a metal spoon warms up faster than a wooden spoon of the same size.

A storage heater in a classroom in Limerick warms the air next to it. The warm air rises and cooler air moves in to replace it.

1. a) Name this method of heat transfer.
2. b) Explain, in terms of density and the motion of particles, why the warm air rises.
3. c) Explain why convection cannot occur in a solid.

On a sunny day, a student standing on Dollymount Strand in Dublin feels the warmth of the Sun on her face.

1. a) Name the method by which energy travels from the Sun to the Earth.
2. b) Explain why this method can transfer energy through the vacuum of space, whereas conduction and convection cannot.
3. c) State why a white house reflects more of this energy than a dark-coloured house does.

A copper rod of length $0.50\ \text{m}$ and cross-sectional area $2.0\times10^{-4}\ \text{m}^2$ has one end in boiling water at $100\,^\circ\text{C}$ and the other end in an ice bath at $0\,^\circ\text{C}$. The thermal conductivity of copper is $k = 400\ \text{W m}^{-1}\text{K}^{-1}$. Assume no energy is lost from the sides of the rod and that the rate of energy flow is given by $\dfrac{Q}{t}=\dfrac{kA\Delta T}{L}$.

1. a) Calculate the rate of energy flow along the rod.
2. b) Calculate the energy transferred in $5.0$ minutes.
3. c) The copper rod is replaced by a steel rod of identical dimensions with $k = 50\ \text{W m}^{-1}\text{K}^{-1}$. Calculate the new rate of energy flow.

A hot-water tank in a house in Cork is cylindrical. Heat is lost to the surroundings mainly by conduction through the insulating jacket. The jacket has area $2.4\ \text{m}^2$, thickness $0.080\ \text{m}$ and thermal conductivity $0.040\ \text{W m}^{-1}\text{K}^{-1}$. The water inside is at $60\,^\circ\text{C}$ and the air outside is at $18\,^\circ\text{C}$.

1. a) Calculate the rate of heat loss through the jacket.
2. b) Calculate the energy lost in $24$ hours, in $\text{kWh}$.
3. c) If electricity costs €0.34 per $\text{kWh}$, calculate the daily cost of replacing this lost energy.

A sea breeze often blows onshore on a summer afternoon at Salthill, Galway. Land heats up faster than the sea during the day.

1. a) Explain why the land heats up faster than the sea, referring to specific heat capacity.
2. b) Using the idea of convection currents, explain why the breeze blows from the sea to the land during the day.
3. c) Explain why the direction of the breeze often reverses at night.

A double-glazed window consists of two glass panes, each $4.0\ \text{mm}$ thick with $k_g = 1.0\ \text{W m}^{-1}\text{K}^{-1}$, separated by a $12\ \text{mm}$ layer of air with $k_a = 0.026\ \text{W m}^{-1}\text{K}^{-1}$. The window has area $1.5\ \text{m}^2$. The inside surface is at $20\,^\circ\text{C}$ and the outside surface is at $2\,^\circ\text{C}$. Treat the heat flow as steady conduction through the three layers in series, using thermal resistance $R=\dfrac{L}{kA}$.

1. a) Calculate the thermal resistance of each layer and the total thermal resistance.
2. b) Calculate the rate of heat flow through the window.
3. c) Calculate the rate of heat flow through a single $4.0\ \text{mm}$ pane of the same area under the same temperature difference, and comment on the result.
4. d) Explain why the air gap is a much better insulator than glass, referring to the particle model and to convection.

A black-painted metal cube of side $0.10\ \text{m}$ is at $400\ \text{K}$ in a laboratory at $300\ \text{K}$. It radiates as a black body, and the Stefan–Boltzmann law gives the power emitted as $P=\sigma A T^4$, where $\sigma = 5.67\times10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$.

1. a) Calculate the total surface area of the cube.
2. b) Calculate the power radiated by the cube.
3. c) Calculate the power the cube absorbs from the surroundings at $300\ \text{K}$, and hence the net rate of energy loss by radiation.
4. d) The cube has mass $8.0\ \text{kg}$ and specific heat capacity $900\ \text{J kg}^{-1}\text{K}^{-1}$. Estimate the initial rate of fall of its temperature, and state why this is only an estimate.

A student investigates which of two identical cans of water cools faster: one painted matt black and one polished silver. Each can contains $0.25\ \text{kg}$ of water initially at $90\,^\circ\text{C}$ in a room at $20\,^\circ\text{C}$. After $10$ minutes the black can is at $62\,^\circ\text{C}$ and the silver can is at $71\,^\circ\text{C}$. The specific heat capacity of water is $4,180\ \text{J kg}^{-1}\text{K}^{-1}$. Ignore the heat capacity of the cans.

1. a) Calculate the energy lost by each can in $10$ minutes.
2. b) Calculate the average power lost by each can.
3. c) Explain the difference in the results in terms of emission of radiation.
4. d) The experiment is repeated with each can filled with water and a lid placed on top. Predict and explain the effect on the results, referring to convection and evaporation.