Physics Study Guide/Thermodynamics

Introduction

Thermodynamics deals with the movement of heat and its conversion to mechanical and electrical energy among others.

Laws of Thermodynamics

First Law

The First Law is a statement of conservation of energy law:

$\Delta U=Q-W$

The First Law can be expressed as the change in internal energy of a system ($\Delta U$) equals the amount of energy added to a system (Q), such as heat, minus the work expended by the system on its surroundings (W).

If Q is positive, the system has gained energy (by heating).

If W is positive, the system has lost energy from doing work on its surroundings.

As written the equations have a problem in that neither Q or W are state functions or quantities which can be known by direct measurement without knowing the history of the system.

In a gas, the first law can be written in terms of state functions as

$dU=Tds-pdV$

Zero-th Law

After the first law of Thermodynamics had been named, physicists realised that there was another more fundamental law, which they termed the 'zero-th'.

This is that:

If two bodies are at the same temperature, there is no resultant heat flow between them.

An alternate form of the 'zero-th' law can be described:

If two bodies are in thermal equilibrium with a third, all are in thermal equilibrium with each other.

This second statement, in turn, gives rise to a definition of Temperature (T):

Temperature is the only thing that is the same between two otherwise unlike bodies that are in thermal equilibrium with each other.

Second Law

This law states that heat will never flow from a cold object to a hot object.

$S=k_{B}\cdot ln(\Omega )$

where $k_{B}$ is the Boltzmann constant ($k_{B}=1.380658\cdot 10^{-23}{\mbox{ kg m}}^{2}{\mbox{ s}}^{-2}{\mbox{ K}}^{-1}$) and $\Omega$ is the partition function, i. e. the number of all possible states in the system.

This was the statistical definition of entropy, there is also a "macroscopic" definition:

$S=\int {\frac {\mathrm {d} Q}{T}}$

where T is the temperature and dQ is the increment in energy of the system.

Third Law

The third law states that a temperature of absolute zero cannot be reached.

Temperature Scales

There are several different scales used to measure temperature. Those you will most often come across in physics are degrees Celsius and kelvins.

Celsius temperatures use the symbol Θ. The symbol for degrees Celsius is °C. Kelvin temperatures use the symbol T. The symbol for kelvins is K.

The Celsius Scale

The Celsius scale is based on the melting and boiling points of water.

The temperature for freezing water is 0 °C. This is called the freezing point

The temperature of boiling water is 100 °C. This is called the steam point.

The Celsius scale is sometimes known as 'Centigrade', but the CGPM chose degrees Celsius from among the three names then in use way back in 1948, and centesimal and centigrade should no longer be used. See Wikipedia for more details.

The Kelvin Scale

The Kelvin scale is based on a more fundamental temperature than the melting point of ice. This is absolute zero (equivalent to −273.15 °C), the lowest possible temperature anything could be cooled to—where the kinetic energy of any system is at its minimum. The Kelvin scale was developed from an observation on how the pressure and volume of a sample of gas changes with temperature- PV/T is a constant. If the temperature ( T)was reduced, then the pressure ( P) exerted by Volume (V) the Gas would also reduce, in direct proportion. This is a simple experiment and can be carried out in most school labs. Gases were assumed to exert no pressure at -273 degree Celsius. ( In fact all gases will have condensed into liquids or solids at a somewhat higher temperature)

Although the Kelvin scale starts at a different point to Celsius, its units are of exactly the same size.

Therefore:

Temperature in kelvins (K) = Temperature in degrees Celsius (°C) + 273.15

Specific Latent Heat

Energy is needed to break bonds when a substance changes state. This energy is sometimes called the latent heat. Temperature remains constant during changes of state.

To calculate the energy needed for a change of state, the following equation is used:

Heat transferred, ΔQ (J) = Mass, m (kg) x specific latent heat capacity, L (J/kg)

The specific latent heat, L, is the energy needed to change the state of 1 kg of the substance without changing the temperature.

The latent heat of fusion refers to melting. The latent heat of vapourisation refers to boiling.

Specific Heat Capacity

The specific heat capacity is the energy needed to raise the temperature of a given mass by a certain temperature.

The change in temperature of a substance being heated or cooled depends on the mass of the substance and on how much energy is put in. However, it also depends on the properties of that given substance. How this affects temperature variation is expressed by the substance's specific heat capacity (c). This is measured in J/(kg·K) in SI units.

Change in internal energy, ΔU (J) = mass, m (kg) x specific heat capacity, c (J/(kg·K)) x temperature change, ΔT (K)