To measure temperature, two fixed points are taken; one of them is freezing point of water, known as `text(ice-point)` and other point is boiling point of water, known as `text(steam point)`.
Some temperature scales are given below

(i) `text(Celsius Scale) (°C)` In this scale of temperature, the melting point of ice is taken as 0°C and the boiling point of water as 100°C and the space between these two points is divided into 100 equal parts. This scale was designed by Anders Celsius in 1710.

(ii) `text(Fahrenheit Scale) (°F)` In this scale, the melting point of ice is taken as `32^@F` and the boiling point of water as 212°F and the space between these two points is divided into 180 equal parts. This scale was designed by Gabriel Fahrenheit in 1717.

(iii) `text(Kelvin Scale) (K)` In this scale, the ice point and the steam point (boiling point) are taken as 273 K and 373 K, respectively and the space between these two points is divided into 100 equal parts. It was designed by Kelvin.

(iv) `text(Reaumur Scale) (R)` In this scale, ice point and, boiling point are taken as `0^@R` and `80^@R` respectively. `1^@R` is equal to the 80th part of difference between two points. This scale was designed by R A Reaumur in 1730.

(v) `text(Rankine Scale) (Ra)` In this scale, ice point and steam point are taken as 460° Ra and 672° Ra, respectively. `1^@Ra` is equal to the 212th part of difference between two points.

`text(Relations between various temperature scales)`
`C/5=(F-32)/9 =(K-273)/5 = R/4 = (Ra- 460)/10.6`

The device which measures the temperature of the body, is called thermometer.
Some different types of thermometers are given below

`text(Constant Volume Gas Thermometer)`
If `p_0, p_(100) , p_(tr) ` and `p_t` are the pressures of gas at temperatures `0^@C,100^@C, ` triple point of water and unknown temperature (`t^@C`) respective! keeping the volume constant, then
`t=((p-p_0)/(p_(100) -p_0))text()^@C` or `T=(273.16 p/p_(tr)) K`

`text(Platinum Resistance Thermometer)`
If `R_0, R_(100) , R_(tr) ` and `R_t` are the resistances of a platinum wire at temperatures `0^@C,100^@C, ` triple point of water and unknown temperature (`t^@C`) respective! keeping the volume constant, then
`t=((R-R_0)/(R_(100) -R_0))text()^@C`
or `T=(R_T/R_(tr) xxT_(tr))K=(R_t/R_tr xx 276.16)K`

`text(Mercury Thermometer)`
In this thermometer, the length of a mercury column from some fixed point is taken as thermometric property. Thus,
`t=((l_t-l_0)/(l_(100)-l_0))xx100^@C` or `T=(l_t/l_(tr) xx273.16)K`

A change in temperature of a body causes change in its dimensions. When the body's temperature is increased, body expands in dimensions. It is called thermal expansion.

`text(Linear Expansion)`
(Expansion in Length of a Solid)

Consider a rod of length `l_1` at a temperature `theta_1`. Let it he heated to a temperature `theta_2` and tb increased length of the rod be `l_2`, then

`l_2 = l_1 ( 1 + alpha Delta theta)`

where , `alpha =` coefficient of linear expansion and `theta = theta_2 - theta_1`

`text(Areal Expansion)`
(Expansion in Surface Area)

It `A_1` is the area of solid at `theta_1 °C` and `A_2` is the area at `theta_2 °C`, then

`A_2 = A_1 ( 1 + beta Delta theta)`

where, `beta =` coefficient of areal ( superficial ) expansion and `Delta theta = theta_2 - theta_1`

`text(Volume Expansion)`
( Expansion in Volume)

If `V_1` is volume of solid at `theta_1 °C` and `V_2` is the volume at `theta_2 °C`, then

`V_2 = V_1 ( 1 + gamma Delta theta)`

where `gamma =` coefficient of cubical (volume) expansion and `Delta theta = theta_2 - Delta theta_1`

In in a beaker (container) a liquid is fully filled and if the temperature of the system increases, then because of the fact that `gamma_text(liquid) > gamma_text(solid)`, the expansion in liquid is more than the expansion in solid and thus the liquid overflows from the container. This is termed as apparent expansion of liquid. Consider a vessel of volume `V_o` fully filled with a liquid of coefficient of cubical expansion `gamma_f`. If temperature of the system is increased by `DeltaT`, then

`Delta V_l = V_o gamma_l Delta T , Delta V_c = V_o gamma_c Delta T` where subscript c denotes the container

The volume of overflowing liquid is

`Delta V = V_o(gamma_l - gamma_c) Delta T = V_o gamma_(l c) Delta T`,

where `gamma_(lc) = gamma_l - gamma_c` is termed as the apparent coefficient of cubical expansion.

Dulong and Petit's method In this method, a column of experimental liquid at `t ^oC` is balanced against other column of the experimental liquid at `0 ^oC` is by taking them in U-tube.

Here , `gamma = (h_t - h_o)/( h_0 t)`

water exhibits an anomalous behaviour. It contracts on heating between 0°C and 4°C. But it shows normal behaviour above 4°C: i.e. it expands above 4°C. For this reason, water has maximum density at 4'C (see graph).

Since, `pV = nRT`

So, at constant pressure,

`p* Delta V = n R * Delta T`

So, `(Delta V)/V = (Delta T)/T`

or `gamma = 1/(Delta T) * ((Delta V)/V) = 1/T`

In expansion of gases, there are two coefficients

(i) Volume Coefficient `(gamma_v)` The change in volume of gas per unit volume per unit degree celsius at constant pressure is known as coefficient of volume expansion.

(ii) Pressure Coefficient `(gamma_p)` The change in pressure of gas per unit degree celsius at constant volume is known as pressure coefficient.

• If the temperature and pressure of gas is constant, then `P_1/P_2 = m_1/m_2` ,where `P_1 ` and `P_2` are pressure of gas.

• If same volume jar having (`P_1` and `P_2`) pressure and ( `T_1` and `T_2`) temperature then, `P = (P_1T_2 + P_2T_1)/(T_1 + T_2)` ( after joining both jar )

Heat is a form of energy that flows from one body to another because of temperature difference between them.
The SI unit of heat is joule U) and the CGS unit of heat is calorie (cal).

One caloric is defined as the heat energy required to raise the temperature of one gram of water through 1°C

1 Calorie = 4. 18 J

The amount of heat required to raise the temperature of 1 g of a substance by 1 °C is called the specific heat of gas.

It is represented by s. Its unit is cal/g°C or joule/g°C.

`s = Q/(m Delta t)`

where Q = amount of heat given to the substance

m = mass of the substance

`Delta t =` rise in temperature

The amount of heat required to raise the temperature of 1 mole of a gas by 1° C is called molar specific heat.

There are two types of molar specific heat

(i) Molar specific heat at constant volume (`C_v`)

It is defined as the amount of heat required to raise the temperature of 1 mole of the gas through 1° C (or 1 K). When its volume is kept constant. It is denoted by `C_v`.

(ii) Molar specific heat at constant pressure `(C_p)`

It is defined as the amount of heat required to raise the temperature of 1 mole of the gas through 1° C (or 1 K), when its pressure is kept constant. It is denoted by `C_p`.

If specific heat at constant pressure `(C_p)` is greater the specific heat at constant volume (`C_v` ), then molar specific heat, `C_p - C_v = R`

where, R = gas constant and its volume is 1.99 `~~ 2 cal mol^-1 K^-1` and this relation is called Mayer's

The amount of heat required to change the state of unit mass of a substance at constant temperature is called latent heat of the substance. If mass m of a substance undergoes a change from one state to another, then the amount of heat required for the process is

`Q = mL`

Where, L is the latent heat of the substance. The SI unit of latent heat is J `Kg^-1` and the CGS unit of latent heat is `cal g^-1`.

There are two types of latent heat

`(i) text(Latent heat of Fusion)` The amount of heat required to change the state of unit mass of a substance from solid to liquid at its melting point is called latent heat of fusion.
In case of ice the latent heat of fusion of ice is `80 \ \cal/gm`

`(ii) text(Latent heat of vaporisation)` The amount of heat required to change the state of unit mass of a substance from liquid to vapour at its boiling point is called latent heat of vaporisation.
In case of water the latent heat of vaporisation is `536 \ \cal/gm.`

There are some important terms related to change of state are given below

(i) Melting and Melting Point

The process of change of state from solid to liquid is called melting. The temperature at which solid starts to liquify is known as the melting point of that solid.
The melting point of a substance at atmospheric pressure is called normal melting point.

(ii) Fusion and Freezing Point

The process of change of state from liquid to solid is called fusion. The temperature at which liquid starts to freeze is known as the freezing point of the liquid.

(iii) Vaporisation and Boiling Point

The process of change of state from liquid to vapour (or gas) is called vaporisation. During the change of state (completely), tbe temperature remains constant which implies both liquid and vapour are at the thermal equilibrium. The temperature at which the liquid starts to evaporate is called the boiling point of the liquid.

(iv) Sublimation

The process of change of state directly from solid to vapour (or gas) is known as sublimation. There is no matter of liquid state of substance. The reverse process of sublimation is not possible e.g., camphor, nepthalene balls etc.

The heat capacity of a body is defined as the amount of heat required to raise its temperature through one degree.

`:.` Heat capacity = Mass x Specific heat

`S = mc`

The SI unit of heat capacity is `JK^-1`

The water equivalent of a body is defined as the mass of water which requires the same amount of heat as is required by the given body for the same rise of temperature.

Water equivalent = Mass x Specific heat

`w = mc`

The SI unit of water equivalent is kg.

The branch of physics that deals with the measurement cf heat is called calorimetry. The principle of calorimetry states that the heat gained by the cold body must be equal to the heat lost by hot body, provided there is no exchange of heat with the surroundings.

Heat gained = Heat lost

This principle is a consequence of the law conservation of energy.

This principle is a consequence of the law of conservation of energy.

All matter is trade up of molecules. The molecules of a gas are in state of rapid and continuous motion. Their ·velocity depends on temperature. Using this molecular motion, various properties of a gas like temperature, pressure, energy etc can be explained. Hence, this theory is called kinetic theory of gases.

Kinetic theory of gases was developed by Claussius and Maxwell.

`text( Assumptions of Kinetic Theory of Gases )`

The entire structure of the kinetic theory of gases is based on the following assumptions

• All gases consist of molecules. The molecules are rigid, elastic spheres identical in all respects for a given gas and different for different gases.

• The size of the gas molecules is very small as compared to the distance between them.

• The molecules of a gas are in a state of continuous random motion, moving in all directions with all possible velocities.

• During the random motion, the molecules collide with one another and with the walls of the vessel.

• The collisions are perfectly elastic and there are no forces of attraction or repulsion between the molecules.

• Between two collisions a molecule moves in a straight path with a uniform velocity.

• The collisions are almost instantaneous i.e., the time of collision of two molecules is negligible as compared to time interval between two successive collisions.

• Inspite of the molecular collisions, the density remains uniform throughout the gas.

Mass (m), volume (V ), pressure (p) and temperature (T) of a gas are the measurable properties. The Law's which inter-relate these properties, are called gas Laws. Let's discuss the various gas laws which give the between measurable properties of gases.

`text(Boyle's law)`

It states that for a given mass of an ideal gas at constant temperature (called isothermal process), the volume of a gas is inversely proportional to its pressure, i.e.

`V prop 1/p`

(where, V = volume, p = pressure, m = mass and T = temperature or pV =constant)

or `p_1V_1 = p_2V_2 = p_3V_3 = ...`

This law can also be shown graphically as

`text( Charles' Law )`

It states that for a given mass of an ideal gas at constant pressure, (called isobaric process) volume of a gas is directly proportional to its absolute temperature

i.e. `V prop T` [ if m and p are constant ]

or `V/T` = constant or ` V_1 /T_1 = V_2/T_2`

This law can also be shown graphically as

`text( Gay-Lussac's Law or Pressure Law)`

It states that for a given mass of an ideal gas at constant volume (called isochoric process), pressure of a gas is directly proportional to its absolute temperature

i.e `p prop T` [ if m and V are constants ]

or `p/T = ` constant

or `p_1/T_1 = p_2/T_2`

Here , temperature is in kelvin

This law can also be shown graphically as

An ideal or a perfect gas is that gas which strictly obey the gas law, (such as Boyle's law , Charle's law , Gay lussac's law etc )

Following are the characteristics of the ideal gas

(i) The size of the molecule of an ideal rs zero, i.e., each molecule of the ideal gas is a point mass with no dimensions.

(ii) There is no force of attraction or repulsion amongst the molecules of an ideal gas.

`text(Equation of State or Ideal Gas Equation)`

The equation which relates the pressure (P), volume (V) and temperature (T) of the given state of an ideal gas is known as idcil gas equation or equation of state. For 1 mole of gas `(PV)/T =R` (constant ) `=> PV =RT`

Where , `R = ` universal gas constant

`text(Vander Waal's Gas Equations)`

For 1 mole of gas `( P + a/V^2) (V - b ) = RT`

For `mu` moles of gas `( P + (a mu^2)/V^2) ( V - mu b ) = mu RT`

Here, a and b are constant i.e. called Vander Waal's constant.

Real gases obey this equation at high pressure and low temperature.

(i) Critical temperature `(T_c)` The maximum temperature below which a gas can be liquefied by pressure done is called critical temperature and it is characteristic of the gas. A gas cannot be liquefied, if its temperature is more than critical temperature.

e.g. `CO_2(31.1°C), O_2 (- 118°C), N_2 (- 147.1°C)` and `H_2O (374.1 °C)`.

(ii) Critical pressure (`P_c)` The minimum pressure necessary to liquify a gas at critical temperature is defined as critical pressure.

e.g. `CO_2` (73.87 bar) and `O_2` (49.7 atm).

(iii) Critical volume (`V_c`) The volume of 1 mole of gas at critical pressure and critical temperature is defined as critical volume.

e.g `CO_2 ( 95 xx 10^-6 m^3)`

Molecules of gases collide with each other and also collide with the walls of the vessel. Thus, gas applies a pressure on the walls of the container, this pressure is called gaseous pressure.

`p =1/3 (mn)/V barv^2`

`=> P =1/2 rho barv^2`

where, m = mass of one molecule,
n= number of molecules of the gas,
V = volume of the vessel,
` bar v^2 = ` root mean square velocity
and `rho =` density of gas