Chapter 7: Thermal physics and matter

The chapter problem: the pressure cooker

A pressure cooker is a strong pan with a lid that clamps shut. A valve in the lid holds the pressure inside higher than the pressure of the air. A cook uses one to cook food faster.

These are the facts to use all the way through the chapter.

• The cooker holds 1.50 kg of water at 20 °C.
• The water boils at 121 °C, because the pressure inside is higher than normal.
• The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹.
• The specific latent heat of vaporisation of water is 2.26 × 10⁶ J kg⁻¹.
• The steam above the water fills a space of volume 2.00 × 10⁻³ m³.
• That steam is at a pressure of 2.00 × 10⁵ Pa and a temperature of 121 °C. Treat the steam as an ideal gas.
• The molar gas constant is R = 8.31 J K⁻¹ mol⁻¹, the Boltzmann constant is k = 1.38 × 10⁻²³ J K⁻¹, and the Avogadro constant is N_A = 6.02 × 10²³ mol⁻¹.
• The cooker boils for 12 minutes, and in that time 0.050 kg of water turns into steam.

By the end of the chapter you will find the energy needed to heat the water and to turn some of it into steam. You will find how many moles and how many molecules of steam are in the space. You will find the average kinetic energy of a steam molecule and its rms speed. Then you will explain why the cooker reaches 121 °C, and why the lid is clamped shut.

First contact: no working yet. Predict. The lid is clamped shut, so the steam cannot escape. As the water is heated, what happens to the pressure inside the cooker? Do you think the water can get hotter than 100 °C before it boils? Write down your answers and one sentence of reasoning.

By the end of this chapter you will be able to

• explain what internal energy is, and how it differs from temperature;
• use $E = mc\Delta\theta$ for the energy that changes a temperature;
• find a specific heat capacity from a heating experiment;
• explain what a change of state is, and why the temperature stays constant;
• use $E = mL$ for the energy that changes a state;
• read a heating curve, and explain its flat parts;
• describe the ideal gas model and its assumptions;
• use the gas laws for a fixed mass of gas;
• convert between the Celsius and kelvin scales;
• explain what absolute zero is;
• use $pV = nRT$ and $pV = NkT$;
• explain the pressure of a gas in terms of molecular collisions;
• use $pV = \dfrac{1}{3}Nm(c_{\text{rms}})^2$;
• find the average molecular kinetic energy and the rms speed of a gas;
• describe how to test Boyle's law.

Where it is used

A chef uses a pressure cooker to raise the boiling point of water and cook food faster. A power station boils water into steam and uses the steam to turn a turbine. A weather forecaster explains why a balloon expands as it rises into lower pressure. A nurse follows the safe pressure limits printed on a gas cylinder, because a warm cylinder holds a higher pressure. A fridge moves energy from the food compartment to the room by boiling and condensing a refrigerant. Every engine that burns fuel has to manage the heat it produces.

Your turn to connect it

Think of a time you have seen something heat up or change state. You could have watched ice melt in a drink, felt a metal spoon warm up in soup, or noticed that a bicycle pump gets hot as you use it. Write down two examples. For one of them, say where you think the energy came from and where it went.

Roadmap

1. 7.1 Internal energy and specific heat capacity
2. 7.2 Ideal gases and molecular kinetic theory
3. Review