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1 Radiation and temperature Specification reference: P6.3 Black body radiation (physics only) Aims This is an activity that has been designed to help you improve your literacy skills. In this activity you will learn more about the relationship between radiation, temperature, and black bodies. You will practise answering questions that involve some of the key command words and scientific terms that you will encounter when trying to explain the relationship between the temperature of a body and the nature of the radiation it emits. Learning outcomes After completing this worksheet, you should be able to: describe the relationship between the temperature of a body and the radiation it emits state what is meant by a black body explain the temperature of a body based on the energy it emits and absorbs. Setting the scene The temperature of a body is dependent on a number of factors, one of which is the amount of energy that is emitted or absorbed by the body. In this activity you will consider the relationship between radiation and temperature and you will see why the temperature of a body changes as a result of the energy it emits and absorbs. Task Read the information about radiation and temperature and then answer the questions that follow. Radiation and temperature The three main methods of thermal energy transfer are called conduction, convection, and radiation. In conduction, energy is transferred through electron and lattice vibrations. The energy is passed from atom to atom from the hotter part of the substance to the cooler part. In convection, energy transfer occurs via the circular motion of particles within liquids or gases. The gases rise when warm and then cool and sink when they are further from the heat source. In radiation, thermal energy is transferred by the absorption or emission of electromagnetic radiation, such as the infrared radiation from the Sun to the Earth. If a body radiates more thermal energy than it absorbs each second then it will cool down. Conversely, if a body absorbs more thermal radiation than it emits per second then it will get hotter. This resource sheet may have been changed from the original. 1
2 Electromagnetic radiation All bodies with a temperature greater than absolute zero radiate energy. Absolute zero is the temperature at which there is no molecular or atomic random motion. It is denoted by a temperature of 0 Kelvin, which is equal to C. To convert from K to C you need to subtract 273. To convert from C to K, you do the opposite. To determine the outgoing radiation power of a hot object, you use the Stefan Boltzmann Law which states, in equation form: P σat 4 where P is power in watts, W; σ is the Stefan Boltzmann constant, W/m 2 K 4. and T is the surface temperature of the radiating body in kelvin, K. So if absolute temperature (in Kelvin) doubles, radiated power increases by a factor of sixteen. Also, changes in temperature alter radiation peak wavelengths. Temperature increases move peak radiation to smaller wavelengths and viceversa. Wien s Law Wien s law, another law of physics, explains the relationship between an object's temperature and the wavelength it emits, and is expressed mathematically as: max constant or max T T The wavelength at which maximum radiation is emitted is expressed by the Greek letter (lambda). T is the object s absolute temperature in Kelvin, and the value of the constant is m K. The higher the object s temperature, the shorter the peak wavelength will be. Wien s law explains why the hot sun emits radiation at shorter wavelengths, with the peak emission in the visible region of the spectrum, whereas the cooler Earth emits almost all of its energy at longer wavelengths in the infrared region of the spectrum. For this reason, solar radiation is often referred to as shortwave radiation, and terrestrial radiation as longwave radiation. It also explains why the Sun radiates light whereas the Earth does not. Questions 1 a State the three methods of thermal energy transfer This resource sheet may have been changed from the original. 2
3 b Describe an example of each of the three methods of thermal energy transfer Convert the following temperatures: a 300 K to C b 150 C to K 3 What will happen to the temperature of a body if the rate at which it radiates energy is equal to the rate at which it absorbs energy? Explain your answer. 4 Use the equation P σat 4 to show that if the surface temperature of a star doubles then its radiative power will increase by a factor of a What is the relationship between the temperature of a star and the peak wavelength of the radiation that it emits? This resource sheet may have been changed from the original. 3
4 b If the surface temperature of a star is 8000 K then what will be the peak wavelength that it emits? c If the surface temperature of a star is 8000 K then what will be the power output if it has a radius of m? 6 The graph below shows how power varies with wavelength for bodies at different temperatures. Use the information on the graph, and the equations in the text, to answer the following questions: a What is the peak wavelength (the wavelength that corresponds to the peak of the curve) for the Sun if it has a surface temperature of 5777 K? This resource sheet may have been changed from the original. 4
5 b What is the ratio of the areas beneath the curves for a body at 1000 K compared with a body at 3000 K? 7 If the cosmic microwave background radiation (CMBR) from the Big Bang has a temperature of 2.7 K, what is its wavelength? 8 a Explain why the colour of a star depends on its temperature. b When an electric hob is switched on it is initially warm but not visible, then it begins to show a dull red, then gets orange and eventually white. Explain why this happens. This resource sheet may have been changed from the original. 5
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