doPhysics · Thermal Physics 1
Calorimetry and Change of State
Heat as energy that flows, its units and the heat to warm a body, \(Q = mc\Delta T\). The latent heat of melting and boiling, and where that energy goes. Heating curves read slope by slope, the principle of calorimetry, and mixtures of ice, water and steam.
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Why this chapter
Why this chapter exists
A thermometer tells you how hot a body is, but not how much energy it took to get there. That second question decides how long a kettle takes and why the sea stays cool at noon. It also explains why steam scalds and why a pressure cooker saves gas. This chapter measures heat. It starts with the heat that warms a body, then the hidden heat of melting and boiling, when the thermometer stands still. Then it puts them together in one law of accounts: in an insulated box, heat lost equals heat gained. With it you can predict the final state of any mixture of ice, water and steam.
You will learn
By the end of this chapter you will
- Define heat, the calorie and the joule, and use Joule's result that 4.2 J of work gives 1 cal of heat.
- Find the heat to warm a body with \(Q = mc\Delta T\), and use heat capacity, molar heat capacity and water equivalent.
- Use \(Q = mL\) for melting and boiling, and explain why the temperature stays fixed during a change of state.
- Explain evaporative cooling, and how pressure moves the boiling point in a pressure cooker and in Ladakh.
- Read a heating curve: the specific heat from each slope, the latent heat from each plateau, and compare two substances on one graph.
- State the principle of calorimetry and find a specific heat by the method of mixtures.
- Compare the heats first, then find the final state of a mixture of ice, water and steam.
Before you begin
Before you begin
From the chapter on temperature, you should know the Celsius and Kelvin scales and what a thermometer measures. From Mechanics, you should know work, kinetic and potential energy, power as energy per second, and the conservation of energy.
Lessons
1
Heat and Specific Heat
Heat is energy that flows because of a difference in temperature. Its units, the joule and the calorie, and Joule's proof that work and heat are the same thing. The heat to warm a body, \(Q = mc\Delta T\), and why water warms so slowly. Heat capacity, molar heat capacity and the water equivalent of a calorimeter.
Heat and its unitsSpecific heat capacityHeat capacity and water equivalent
2
Latent Heat: Energy with No Rise in Temperature
While ice melts or water boils, heat goes in and the temperature stays fixed. The heat of a change of state, \(Q = mL\), where that energy goes, and why steam scalds. Evaporation at any temperature cools a clay pot, and pressure moves the boiling point in a pressure cooker and on the heights of Ladakh.
Latent heatWhere the energy goesEvaporation boiling and pressure
3
Reading a Heating Curve
Ice heated steadily until it becomes steam draws a staircase of slopes and plateaus. Each slope gives a specific heat, each plateau a latent heat, and one graph of two substances tells which melts higher, holds more heat per kelvin, and needs more heat to melt.
The heating curve of waterSlopes and plateausTwo substances on one graph
4
The Principle of Calorimetry
In an insulated vessel the heat lost by the hot bodies equals the heat gained by the cold ones. The final temperature of a mixture, the calorimeter and its parts, the method of mixtures for finding a specific heat, and three liquids mixed in pairs.
Heat lost equals heat gainedThe method of mixturesThree liquids mixed pairwise
5
Mixing Ice, Water and Steam
When ice or steam is mixed with water, first compare the heats available and needed. The comparison decides whether the mixture ends at 0 °C with ice left, above 0 °C with all the ice melted, or at 100 °C with steam left. Then one equation gives the answer.
Check the heat before solvingWhen all the ice meltsSteam into water
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%The Workbook
Questions to solve on paper, marked by you.
Glossary
The key words of this chapter, with the meaning this chapter gives them.
- boiling point
- The temperature at which a liquid boils, forming bubbles of vapour throughout. It rises with the pressure above the liquid; for water at 1 atm it is 100 °C.
- calorie
- The heat needed to warm one gram of water by one degree Celsius. In this book \(1\,\text{cal} = 4.2\,\text{J}\). A food Calorie is 1000 calories.
- calorimeter
- An insulated vessel for measuring heat. A thin copper cup with a stirrer and a thermometer sits inside a jacket, with an air gap and a lid.
- change of state
- A change from solid to liquid, liquid to vapour, or back. At a given pressure it happens at a fixed temperature, with heat taken in or given out.
- cooling curve
- A graph of temperature against time for a substance that is cooling. A flat part marks the freezing point, where the latent heat given out replaces the heat lost.
- evaporation
- The escape of the fastest molecules from the surface of a liquid, at any temperature. It takes latent heat from the liquid, which cools.
- heat
- Energy that flows from one body to another because of a difference in their temperatures. A body gains or loses heat; it does not contain it.
- heat capacity
- The heat needed to warm a whole body by one kelvin, C = mc, in J/K. It belongs to an object, not a material.
- heating curve
- A graph of temperature against time, or against heat supplied, for a substance heated at a steady rate. Slopes show one state warming; flat parts show a change of state.
- latent heat
- The heat needed to change the state of one kilogram of a substance at a constant temperature, \(Q = mL\), in J/kg. The same heat is given out in the reverse change.
- latent heat of fusion
- The latent heat for melting a solid, \(L_f\). For ice it is \(3.34 \times 10^5\,\text{J/kg}\), or 80 cal/g.
- latent heat of vaporisation
- The latent heat for boiling a liquid, \(L_v\). For water it is \(2.26 \times 10^6\,\text{J/kg}\), or 540 cal/g.
- mechanical equivalent of heat
- The work that produces one unit of heat, J = W/Q = 4.2 J/cal, found by Joule with a paddle wheel. It is a conversion factor between two units of energy.
- melting point
- The temperature at which a solid turns into a liquid at a given pressure. It is also the freezing point of the liquid; for ice at 1 atm it is 0 °C.
- method of mixtures
- Finding a specific heat by dropping a hot body into a calorimeter of water. The heat it loses is set equal to the heat the water and vessel gain.
- molar heat capacity
- The heat needed to warm one mole of a substance by one kelvin. It is Mc, where M is the molar mass; for water 75.6 J/(mol K).
- principle of calorimetry
- In an insulated vessel, the heat lost by the hotter bodies equals the heat gained by the colder bodies. It is energy conservation for heat.
- specific heat capacity
- The heat needed to warm one kilogram of a material by one kelvin, \(c = Q/(m\Delta T)\), in J/(kg K). Water's is 4200 J/(kg K).
- thermal equilibrium
- The state of bodies in contact that have reached one common temperature, so that no more heat flows between them.
- water equivalent
- The mass of water that has the same heat capacity as a body, \(W = mc/c_w\). A 200 g copper calorimeter has a water equivalent of 19 g.