Heat And Thermodynamics

Brownian Motion

In 1827, Robert Brown discovered that fine pollen grains suspended in water were in a state of constant movement, describing small irregular paths but never stopping. This effect is called Brownian motion.

Brownian motion is observed with many kind of small particles suspended in both liquids and gases.

Brownian motion is due to the unequal bombardment of the suspended particles by the molecules of the surrounding medium.

The Celsius (or centigrade) temperature scale:

To define the Celsius temperature scale two "reliable" temperatures are used. These are, the melting point of pure ice, which gives us the lower fixed point at the scale and the boiling point of point water (at atmospheric pressure) which gives us the upper fixed point. The difference between these two points is divided into 100 equal intervals called degrees.

This choses scale is a purely arbitrary scale.

The Kelvin or absolute scale of temperature is a more fundamental scale.

The size of the degree on the Kelvin scale is the same as on the Celsius scale but the zero corresponds to a very different temperatures. To convert temperatures on the Celsius scale to temperatures on the Kelvin scale simply add 273 to the Celsius reading.

Absolute zero:

Absolute zero is that temperature at which the volume of the gas becomes zero if pressure is a constant. The value of absolute zero is - 273.15 °C.

Thermal expansion:

Let coefficient of linear expansion =

Coefficient of superficial expansion = =

Coefficient of cubical expansion = =

Principle of calorimetry:

Whenever two bodies at different temperatures are mixed, heat lost by the body at higher temperature is gained by the body at lower temperature.

Heat lost = heat gained

If temperature of body changes but state of the body does not change, specific heat of the material of body is relevent whether heat is lost or gained.

Amount of heat lost or gained =

Where denotes change of temperature and m denotes mass of the body of specific heat the body of specific heat s.

If state of body changes (from solid to liquid to solid or liquid to gas or gas to liquid) but temperature of body does not change, amount of heat exchanged = mL where L = latent heat of the material which undergoes change of state.

If change of temperature as well as change of state both occurs in a system, amount of heat exchanged = + mL.

Conversion of ice at 0 K into steam at 100 K is example of such a change.

The heat capacity of a body:

The larger pan of water needs a greater quantity of energy to cause its temperature to change by a given amount. We say that the larger pan has a greater heat capacity than the smaller one.

The heat capacity of a body is the quantity of energy needed to cause its temperature to change by 1 °C.

The units of heat capacity are or

The heat capacity of a body depends on

  1. what substance (s)it is made of and
  2. the masses of the different substances in the body.

The specific heat capacity of a substance is the quantity of energy needed to change the temperature of 1 kgthe temperature of 1 kg of the substance by 1°C.

The units of specific heat capacity are or .

To calculate the quantity of energy, Q, needed to change the temperature of m kg of a substance of specific heat capacity, s, by C we use the equation Q = .

To change the temperature of a body means to change the average kinetic energy of its particles.

The particles of different substances have different masses. The number of particles in 1 kg of a substance depends on the mass of those particles. This explains why different substances have different specific heat capacities.

The specific heat capacity of water is high compared with most other substances:

= 4200 (approximately).

Gases are said to have two principal specific (or molar) heat capacities:

  1. the specific (or molar) heat capacity at constant volume,
  2. the specific (or molar) heat capacity at constant pressure,

It should be clear that > and that difference between them is given by

= R,

Where R is the constant.

The workdone by force is W = Fs = PAs

But As is the change in the volume occupied by the gas, . Therefore W = .

When the volume of a gas increases, work is done by the gas.

When the volume of a gas decreases, work is done on the gas by an external force.

However, if the temperature is increased and the gas is allowed to expand, work will be done. In this case, extra energy will have to be supplied to do this work.

A "P-V diagram" is a graph showing changes in the pressure and volume of a sample of gas. It is useful to be able to recognise various types of change of the state of a gas from a P-V diagram.

Four examples are given below.

  1. Change of P (and T) at constant volume; an isovolumetric or isochoric change.
  2. Change of V (and T) at constant pressure; an isobaric change.
  3. Change in P and V at constant temperature; an isothermal change.
  4. Change in P and V in an insulated container (no heating of the gas); an adiabatic change.

In practice, changes of state do not quite follow any of these ideal paths. However, approximate isothermal, adiabatic etc changes can occur.

For an iso-volumetric change, heat the gas in a fixed volume container (one made of a material having a low thermal expansivity)

For an isobaric change, trap a small quantity of the gas in a tube using a thread of mercury (or other liquid , as in experiment 6TP) and heat it slowly

For an isothermal change, compress (or expand) the gas slowly in a container of high thermal conductivity.

For an adiabatic change, compress (or expand ) the gas rapidly in a container of low thermal conductivity.

In case of isothermal relation between P and V for perfect gas is PV = constant.

In case of isothermal relation between P and V for perfect gas is PV = constant.

In case of adiabatic relation between P and V for perfect gas is = constant, where = .

Slopes of isothermal and adiabatic curves are

= (for isothermal)

= (for adiabatic)

As > 1 , therefore adiabatic curve at any point is steeper then the isothemal curve at that point.

Workdone is an isothermal expansion is

W = or W = .

Workdone in an adiabatic expansion is

W = or, W = .

Internal energy (U) of a system is the energy prosessed by the system due to molecular motion and molecular configuration.

According to first law of thermodynamics, heat given to a system is equal to the sum of increase in its intenal energy and the workdone by the system against the surroundings is

=

In cyclic process, = , = 0.

= 0 + , i.e. heat supplied is equal to workdone.

In isothernal energy U will also constant .i.e. = 0.

= .

i.e. heat supplied in an isothermal change is used to do work against external surroundings.

In adiabatic process, no beat enters or leaves the system. i.e. = 0.

0 = + or, = .

i.e. if gas expands, internal energy and hence temperature will decrease and so the gas will get cooled.


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