Thermal physics :

(i) Heat and temprature

(ii) Kinetic theory of gas

(iii) Thermodyanmics

(iv) Thermal properties of matter

A form of energy.

Propagation of heat: hotter to cooler body.

Mechanical Energy:

(i) Kinetic Energy

(ii) Potential energy

Temprature: Measure which dictates which direction heat flows.

Kinetic Theory of gas temprature : "T"

T $\propto$ average translational kinetic Energy.

Steam Point : Highest of Water

Ice point : Lowest of water

We can measure anything with respect to these two temperature in our Celsius scale.

Average : a huge number of particles, $10^{23}$.

In mechanics, each molecule described by Newton's laws: $m \frac{d^2 \vec{x}}{dt^2} = \vec {F}$

$3 \times 10^{23} \rightarrow$ average description.

Kinetic theory

(i) Distribution

(ii) Gas molecule $\rightarrow$ velocities

Distribution of velocity will give me average properties which will be related to kinetic energy.

Thermodynamics language is a coarse-grained description.

In the macroscopic level we will consider the measurable quantities.

P, T $\rightarrow$ Intensive

V $\rightarrow$ Extensive

Equilibrium : Nothing depends on time.

Ideal gas equation: PV = nRT, where n is number of moles.

Ideal gas

(i) Point particles

(ii) No interaction

(iii) Energy is entirely kinetic

de Broglie wavelength: $\lambda = \frac{h}{p}$

$\lambda = \frac{h}{\sqrt{2mkT}}$

a $\rightarrow$ container ofV, N

$(\frac{V}{N})^{1/3} = a$

$a>> \lambda$

Let us assume that the average kinetic energy of a molecule:$\frac{p^2}{2m} \sim kT$

$p \sim \sqrt{2mkT}$

$\frac{N}{V} = \rho$

Ideal gas is a good approximation when T is high and density is low.

T $\rightarrow$ Constant

PV = const.

Charles law: $V \propto T$

$\Rightarrow PV = nRT \rightarrow$ absolute scale of temprature

$T = 273^{\circ}$

$T \rightarrow 0$

Kinetic Energy of Gas : Microscopic description.

(i) Molecules are moving in all average directions.

(ii) Points particles size, smaller than interatomic distance.

(iii) Any interaction $\rightarrow$ collisions between two molecules.

Consider classical motion, so all these molecules satisfy Newton's laws of motion.

Collisions are elastic collisions which are all dictated by the classical mechanics.

Homogeneous : density is uniform.

Velocities will be having three components ($v_x, v_y, v_z$).

We will consider complete isotropic.

Equilibrium is independent of time.

$x \rightarrow - \infty$ to $\infty$

Average value: $\langle x \rangle = \int x P(x) dx$

Total probability: $\int_{-\infty}^{\infty} P(x) dx=1$

P(x)=Ne

Velocity components are $v_x, v_y, v_z$

$v=\sqrt{v_x^2 + v_y^2 + v_z^2}$

$P(v_x)P(v_y)P(v_z) dv_x dv_y dv_z$

$\sim Ae^{ -a(v_x^2 + v_y^2 + v_z^2)} dv_x dv_y dv_z$

Speed Distribution:

$P(v)dv = Av^2 e^{-bv^2} dv$

Random motion of the particles inside a container.

$PV = \frac{1}{3} m N \bar v^2$

Euation of state of a gas.