Chapter 10 Thermal Physics

Temperature Thermodynamics – branch of physics studying thermal energy of systems Temperature ( T ), a scalar – measure of the thermal (internal) energy of a system SI unit: K (Kelvin) Kelvin scale has a lower limit (absolute zero) and has no upper limit William Thomson (Lord Kelvin) ( )

Kelvin scale Kelvin scale is defined by the temperature of the triple point of pure water Triple point – set of pressure and temperature values at which solid, liquid, and gas phases can coexist International convention: T of the triple point of water is

The zeroth law of thermodynamics If two (or more) bodies in contact don’t change their internal energy with time, they are in thermal equilibrium 0th law of thermodynamics: if bodies are in thermal equilibrium, their temperatures are equal

Measuring temperature Temperature measurement principle: if bodies A and B are each in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other (and their temperatures are equal) The standard temperature for the Kelvin scale is measured by the constant-volume gas thermometer

Constant-volume gas thermometer

Celsius and Fahrenheit scales Celsius scale: Fahrenheit scale: Anders Cornelius Celsius ( ) Gabriel Daniel Fahrenheit ( )

Chapter 10 Problem 3 Convert the following temperatures to their values on the Fahrenheit and Kelvin scales: (a) the boiling point of liquid hydrogen, –252.87°C; (b) the temperature of a room at 20°C.

Thermal expansion Thermal expansion: increase in size with an increase of a temperature Linear expansion: Volume expansion:

Thermal expansion

Chapter 10 Problem 14 A cube of solid aluminum has a volume of 1.00 m 3 at 20°C. What temperature change is required to produce a 100-cm 3 increase in the volume of the cube?

Temperature and heat Heat ( Q ): energy transferred between a system and its environment because of a temperature difference that exists between them SI Unit: Joule Alternative unit: calorie (cal):

Avogadro’s number Mole – amount of substance containing a number of atoms (molecules) equal to the number of atoms in a 12 g sample of 12 C This number is known as Avogadro’s number ( N A ): N A = 6.02 x mol -1 The number of moles in a sample N – total number of atoms (molecules) m – total mass of a sample, m 0 – mass of a single atom (molecule); M – molar mass Amedeo Avogadro ( )

Ideal gases Ideal gas – a gas obeying the ideal gas law: R – gas constant R = 8.31 J/mol ∙ K k B – Boltzmann constant k B = 1.38 x J/K Ludwig Eduard Boltzmann ( )

Ideal gases The gas under consideration is a pure substance All molecules are identical Macroscopic properties of a gas: P, V, T The number of molecules in the gas is large, and the average separation between the molecules is large compared with their dimensions – the molecules occupy a negligible volume within the container The molecules obey Newton’s laws of motion, but as a whole they move randomly (any molecule can move in any direction with any speed)

Ideal gases The molecules interact only by short-range forces during elastic collisions The molecules make elastic collisions with the walls and these collisions lead to the macroscopic pressure on the walls of the container At low pressures the behavior of molecular gases approximate that of ideal gases quite well

Ideal gases

Root-mean-square (RMS) speed:

Translational kinetic energy Average translational kinetic energy: At a given temperature, ideal gas molecules have the same average translational kinetic energy Temperature is proportional to the average translational kinetic energy of a gas

Internal energy For the sample of n moles, the internal energy: Internal energy of an ideal gas is a function of gas temperature only

Chapter 10 Problem 30 A tank having a volume of m 3 contains helium gas at 150 atm. How many balloons can the tank blow up if each filled balloon is a sphere m in diameter at an absolute pressure of 1.20 atm?

James Clerk Maxwell ( ) Distribution of molecular speeds Not all the molecules have the same speed Maxwell’s speed distribution law: N v Δv – fraction of molecules with speeds in the range from v to v + Δv

Distribution of molecular speeds Average speed: RMS speed: Most probable speed:

Questions?

Answers to the even-numbered problems Chapter 10 Problem 28 (a) 3.0 mol (b) 1.80 × molecules

Answers to the even-numbered problems Chapter 10 Problem × 10 5 Pa