Development of Ideal gas law

For gases, the thermal expansion is very large as compared to solids and liquids. For example, the volume of a gas changes appreciably when even a little pressure is applied. Hence the pressure, volume, and temperature need to be stated to describe the condition of a gas. The gas laws provide a relation between any two of the three quantities, while the third is kept constant.

We have,

1. Boyle’s Law-the temperature remaining constant, the volume of a given mass of a gas is inversely proportional to the pressure. Mathematically, if temperature of the gas is constant then PV=constant.
2. Charles’ Law-the pressure remaining constant, the volume of a given mass of gas increases or decreases by a constant fraction of its volume at zero degree Celsius for each rise or fall of one degree Celsius in temperature. Hence, if the gas is at constant pressure, then,

V/T=constant.

It can also be stated as The pressure remaining constant, the volume of the given mass of a gas is directly proportional to its absolute temperature.

1. Gay-Lussac’s Law-the volume remaining constant, the pressure of a given mass of a gas increases or decreases by a constant fraction of its pressure at zero degree Celsius for each rise or fall of one degree Celsius in temperature. The relation is given as,

P/T=constant.

In other words, The volume remaining constant, the pressure of a given mass of gas is directly proportional to its absolute temperature.

### What is a Perfect gas?

In practice, the gases do not obey the gas laws for all values of temperature, pressure and volume due to the intermolecular attraction between gas molecules. A perfect gas is one, whose molecules are free from intermolecular attraction and obeys the gas laws at all values of temperature and pressure.

Perfect gas Equation

It is a culmination of all the equations stated above and gives the following relation,

(P*V)/T=constant.

One mole of a gas at standard temperature and pressure occupies 22.4 litres. The given equation for one mole of a gas translates to, (P*V) =RT, where R is the universal gas constant. The value of R is given as 8.31 J per mole per kelvin.

If V is the volume of one gram of gas then we get,PV=(R/M)*T or PV=rT, where r is the gas constant for one gram of gas and M is the molecular weight of gas.

If the gas contains n moles, then we have,PV=nRT.

The gas equations are all validated by the kinetic theory of gases.

HEAT

We all have the sense of touch and are most familiar with the sensation of hot and cold. Some objects are thought to be hot and some cold, for example, an ice cube is cold and a piece of burning charcoal is hot.

Heat is a form of energy which produces in us the sensation of warmth.

Heat energy possessed by a body is due to the kinetic energy of the molecules and hence heat can be provided to a body to cause changes in various physical properties. The energy can be harnessed and changed into various other forms such as mechanical energy and electrical energy.

Once heat is transferred it becomes the internal energy of a body. This is necessary to understand as the word “heat” is only meaningful as long as energy is being transferred, the terms “heat of a body” or “heat in a body” do not hold any meaning.

As heat is just energy in transit, its SI unit is joule. It also has another unit known as the calorie. The amount of heat needed to increase the temperature of 1 g of water from 14.5 degree Celsius to 15.5 degree Celsius at a pressure of 1 atm is called 1 calorie.

## LAWS OF THERMODYNAMICS

#### What is thermodynamics?

An assembly of an extremely large number of particles having a certain value of pressure, volume and temperature is called a thermodynamic system.

A thermodynamic process is said to take place if the thermodynamic variables of the system change with time. The various types of thermodynamic processes are isothermal, isobaric, isochoric, adiabatic, cyclic.

Thermal equilibrium-Two systems are said to be in thermal equilibrium with each other if they are at the same temperature.

### Zeroth Law of thermodynamics

It states that if there are two systems A and B which are in thermal equilibrium with a third system C, then the systems  A and B must be in thermal equilibrium with each other.

To understand this, let us assume that there are three systems A,B,C. Systems A and B are separated by an adiabatic wall (does not allow heat transfer) and another system C is placed adjoining to both and separated by a diathermic wall(allows heat transfer). There will be no heat exchange between A and B , but there will be an exchange between B and C and A and C. After a time all three systems will reach thermal equilibrium and if the adiabatic wall is removed then there will be no heat exchange between A and B.

### First Law of thermodynamics

The first law of thermodynamics is given as, if an amount of heat dQ is added to a system, a part of it may increase its internal energy by an amount dU, while the remaining part may be used up as the external work dW done by the system.

It is drawn from the law of conservation of energy, which states that, energy can neither be created nor destroyed. The first law ,extends this law to to include heat energy and internal energy of a system.

Thus, if dU, dW, and dQ are all in same units, then,

dQ=dU+dW.

In case a gas is enclosed in a cylinder provided with a frictionless and weightless piston, the equation can also be considered as – dQ=dU+PdV, where P is the pressure and V the volume of gas at initial state.

For a cyclic process, we obtain the equation- dW=PdV as the change in internal energy in a complete cyclic process is Zero.

Similarly, for an isothermal process, we get dQ=dW.

For an adiabatic process we get, dU+PdV=0, dQ=0 , as no heat enters or leaves the system.

Limitations of the first Law

1. It does indicate the direction of transfer, that is, it does not tell us why heat cannot transfer from a cold body to a hot one.

1. It does not tell us anything about the conditions under which heat can be transformed into work.

3. The law also does not indicate why the whole of heat energy cannot be converted into mechanical energy continuously.

### Second Law of thermodynamics

The second law of thermodynamics disallows some processes consistent with the first law

Kelvin’s statement of the second law of thermodynamics- It is impossible to derive a continuous supply of work by cooling a body to a temperature lower than that of its coldest surroundings.

Clausius statement of the second law- It is impossible for a self- acting machine, unaided by any external agency, to transfer heat from a body at lower temperature, to another at higher temperature.

Both these statements are used to draw the same inference. Violating one statement leads to violating the other. The second law is used to design the Carnot’s heat engine and the principle of a refrigerator is based on it, where refrigerator works in the opposite direction as Carnot’s heat engine.

A reversible process-A process that can be made to work in the reverse direction, if we change conditions such that all changes while working in the direct process are exactly opposite is known as the reversible process.

Conditions for a reversible process-

1. The process should take place very slowly so that the system is always in thermal and mechanical equilibrium.

2. The system should be free from forces such as friction, the viscosity that is dissipative.

The Carnot’s heat engine is a device that transforms heat into mechanical work continuously and it’s efficiency depends on the temperature of source and sink only. As the refrigerator is known to take heat from the sink(its contents) at lower temperature which it rejects to the atmosphere, it has to perform mechanical work in doing so. A refrigerator acts as an electrical heater of efficiency greater than 1. In this manner, it works in the reverse direction of the Carnot’s cycle.

#### TEMPERATURE

The degree of hotness of a body is called temperature.

The physical sensations of hot and cold are not sufficient. For example, if we place our left hand in cold water and right in hot water and then place both in water at room temperature, the water will fell hot to our left hand and cold to our right hand.

If two water reservoirs having water are interconnected then water will flow from the higher level to lower level, irrespective of the amount of water.Similarly, heat flows from a body at higher temperature to that at a lower temperature.

Hence, we can understand that temperature is a condition that determines the direction of flow of heat when two bodies are mixed together.

There are various scales of temperature such as – Celsius, Fahrenheit, Kelvin, and Reaumer.

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