# 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 `<b>`{=html}First Law`</b>`{=html} is a statement of conservation of
energy law:

+----------------------------------+
| ```{=html}                       |
| <center>                         |
| ```                              |
| `<big>`{=html}$\Delta U = Q - W$ |
+----------------------------------+

The `<b>`{=html}First Law`</b>`{=html} 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
`<b>`{=html}state functions`</b>`{=html} 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

+----------------------------------+
| ```{=html}                       |
| <center>                         |
| ```                              |
| `<big>`{=html}$dU = T ds - p dV$ |
+----------------------------------+

### 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:

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  *If two bodies are at the same temperature, there is no resultant heat flow between them.*
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An alternate form of the \'zero-th\' law can be described:

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  *If two bodies are in thermal equilibrium with a third, all are in thermal equilibrium with each other.*
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This second statement, in turn, gives rise to a definition of
Temperature (T):

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

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  *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.

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  *Change in internal energy,*Δ*U (*J*) = mass, m (*kg*) x specific heat capacity, c (*J*/*(kg·K)*) x temperature change,*Δ*T (*K*)*
  ------------------------------------------------------------------------------------------------------------------------------------
