Temperature and Heat Capacity

Principles of Thermometry | taught by Math Arena

Course description


This course is targeted at Singapore Cambridge GCE O level students, but is also relevant to IGCSE students and Singapore's Integrated program students.

Did you know you can heat things up by shooting bullets at them (or by dropping them on the floor)? In fact, if we make a number of assumptions, we can actually calculate how much their temperature will change when we do so! Are you interested to find out how to do that? Then jump right in! We will also be exploring the different characteristics and properties of thermometers - the instruments that help us measure temperature. And not just the boring old thermometers that you stick in your mouth (although there's no way we could not cover those too). You might just be surprised.

Course Content

You will learn:

  • What types of thermometers are good for what things
  • How to measure temperature with a thermometer that has absolutely no markings whatsoever
  • What heat capacity is and how to use it
  • How much water you can boil by dunking hot metal in it
  • How to maximise the amount of heat gained by shooting things (or by dropping them on the floor)

A link to the full O level Physics syllabus can be found here

Course Prerequisites

You will need to know:

  • A little bit of Work Energy and Power (how to calculate kinetic energy and gravitational potential energy)
  • How to watch videos on your computer
Math Arena
Math Arena

The instructor is from Math Arena.The instructor is absolutely passionate about teaching and you'll find the lessons engaging and ultimately rewarding.

Course Curriculum

Calibrating thermometers
Q13 What is ice point ?
Q14 What is an essential requirement for a thermometer, which depends on a particular thermometric property, to measure a particular temperature range?
Q15 To calibrate a thermometer, without using another thermometer, fixed points are required. Which statement is correct?
Q16 A student is given a thermometer that reads -1°C for the lower fixed point and 99°C for the upper fixed point. Which of the following describes the temperature recorded by the thermometer before and after heating and the temperature difference?
Q17 The mercury thread in a thermometer stands at the 5 °C mark at ice-point and at the 95 °C mark at the steam-point. What will be its reading when placed in contact with a body of temperature of 40 °C?
Q18 The distance between the 10°C mark and the 90°C mark on a mercury thermometer is 25 cm when the mercury level is 5 cm below the 90°C the temperature is approximately
Q19 A student using an unmarked liquid-in-glass thermometer puts the bulb into melting ice, then into steam above boiling water and finally into sea-water. The liquid levels are shown on the diagram. What is the approximate temperature of the seawater?
Q20 The resistance of a piece of platinum wire in pure melting ice is 800 Ω. The resistance of the wire in steam is 910 Ω. What would be the temperature when the wire has a resistance of 1000 Ω?
Q21 A thermocouple indicates 0.1mV at ice point and 2.6mV at 500 °C. What will be the temperature when the thermocouple indicates 3.0mV?
Q22 The length of mercury in the bore of a thermometer is 5.0 cm at 0 °C and 11.0 cm at 60 °C. What is the length in the bore when the temperature is –10 °C?
Heat capacity and specific heat capacity - calculating quantities
The heat capacity equation
Q37 What is the definition of heat capacity?
Q38 Wind is blowing across a cup of hot tea. Determine the time necessary to cool the cup of tea to 55 °C.
Q39 The specific heat capacity of a liquid is measured by immersing a heating coil in a beaker of the liquid. The value calculated for the specific heat capacity of the liquid will be lower than the correct value if
Q40 An immersion heater connected to a kilowatt-hour meter is used to supply heat to 4.0 kg of oil. The initial reading of the kilowatt-hour meter is 10.95 kWh. After heating, the meter reads 11.03 kWh. Find the rise in temperature of the oil.
Q41 Which of the following objects has the biggest temperature increase if 54 000J is supplied to each?
Q42 When a 2.0 kg block of metal at 600°C is immersed in water at its boiling point (100°C), 0.4 kg of steam is produced. The specific heat capacity of the metal is
Q43 An object A has a mass m kg and specific heat capacity C J kg-1 K-1 and temperature = 60°C. An object B has a mass of 2m kg and specific heat capacity 2C kg-1 K-1 and temperature = 30°C. What will be the final temperature reached?
Q44 In an experiment to find the specific heat capacity of a metal, it is found that 5200 J is needed to raise the temperature of a 2 kg block by 20 °C. What value for the specific heat capacity is given by these results?
Q45 The copper blocks X and Y have masses Mx and My respectively. In an experiment the blocks are heated. The results in the experiment shown in the table below. What is the value of Mx/My?
Latent heat and specific latent heat
Q56 A substance that is originally a solid is heated strongly for some time. At one stage, the energy given to the substance is used as latent heat of vaporisation. At this stage, what change does the energy cause?
Q57 A solid substance is placed in a boiling tube and heated steadily. The temperature-time graph of the substance is as shown below. At which portion is the substance absorbing latent heat?
Q58 Two substances X and Y are heated by identical heaters. The graph below shows the variation of temperature with time for the substances. If X and Y are of the same mass, which of the following statements is correct?
Q59 Two solids X and Y of identical mass are heated separately by heaters of equal power. The graphs below show the variation of their temperatures with time. Which of the following statements is/are correct?
Q60 Liquid X and Y of the same mass and temperature are put into a refrigerator to cool down. The graph below shows the variation of the temperatures of the liquids with time. Which of the following statements is/are correct?
Q61 The diagram below shows the apparatus used for finding the specific latent heat of vaporization of water. Which of the following factors will cause the result obtained to be smaller than the true value?
Q62 A kettle rated at 240 V 300 W was used to heat a liquid from 28 °C to 100 °C. The time it took to just boil 500 g of liquid was 8.4 minutes. What is the specific heat capacity of the liquid?
Q63 Two solids, X and Y, of equal masses are melted by heaters of same power ratings at the same time. The variation of their temperatures with time is given in the graph. Which of the following statements is/are true?
Extra Questions
Q1 Use the thermal properties of matter to explain how steam can be more dangerous than boiling water even though both are at 100°C.
Q2 Why does the sea remain cooler than the land in warm weather?
Q3 Why do storage heaters contain bricks of high specific heat capacity?
Q4 Why is water used in many types of heat exchanger?
Q5 When we engage in exercise or strenuous physical work, the body temperature does not rise excessively. Explain.
Q6 (part 1) Specific latent heat of fusion of ice experiment choosing initial and final temperatures and determining the mass of ice
Q6 (part 2) Specific latent heat of fusion of ice experiment calculating the specific latent heat
Q7 A 500 watt electric drill is used to drill a hole in an aluminium block of mass 1 kg. If 80% of the energy used appears as heat in the metal, find the increase in temperature of the aluminium in 20 seconds.
Q8 A car of mass 1800 kg and moving at 25 m s-1 is brought to rest by the application of disc brakes. Find the average increase in temperature of the brakes if each of the four brakes has a mass of 4.5 kg.
Q9 The temperature of 100 g of water was raised from 20 °C to 40 °C in 10 minutes by a heating coil of resistance 5.0 ohms and carrying a current of 2.0 A. Calculate the amount of energy lost to the surroundings.
Q10 Water is being pumped through a central heating system at a rate of 1.15 m3 per hour. The temperature of the water leaving the boiler is 58.0 °C and the temperature of the water returning is 48.0 °C. Calculate the power output of the boiler
Q11 A refrigerator converts 1.3 kg of water at 20 °C into ice at -15 °C in 1 hour. Calculate the total heat removed and the effective power of the refrigerator
Q12 Why does it take so long for a domestic refrigerator to form ice-cubes from a tray of water?
Q13 Microwave oven
Q14 Specific latent heat of vaporisation of water experiment
Q15 (part 1) Ice heating graph explain where the energy is going in each section
Q15 (part 2) Ice heating graph calculating the mass of ice