Thermodynamics and KTG

What is Degree of freedom for matter

They’re the number of independent ways in which a molecule can move (translation motion), spin (Rotational motion), and Vibrate and produce energy

What is the formulae to calculate vibrational degree of freedom

Vibrational DOF = 3N−Translational DOF − Rotational DOF​

where,
N → Number of atoms in the molecule

What is entropy

It is the measure of disorderness in the system

What is Bolt’s constant

It is the measure of energy per molecule

What is the formula for Bolt’s constant

Kb = R/N_A
where,
N_{A →} Avagadro’s number
R → Universal gas constant

What is the formula for molar heat capacity at constant volume

C_v =FR/2
where,
F → Degree of freedom
R → Universal gas constant

What is the relation between molar heat capacity at constant pressure and molar heat capacity at constant volume

1. n*C_p - n*C_v = R
   where,
   C_p → molar heat capacity at constant pressure
   C_v → molar heat capacity at constant volume
   R → universal gas constant

   n → Number of moles

2. C_p /C_v = γ

What is the formula for the ratio that we get between C_p and C_v? What is it called?

γ = 1 + 2/f
where,
f → Degree of freedom

γ → Coefficient of adiabatic process

What is R?

It is the universal gas constant per mole of gas

What is C_m

It is the molar heat capacity

What is the formula for the speed of gas?

√γ*R*T/m
Where,
γ → Coefficient of adiabatic process
R → Universal gas constant
T → Temperature
m → mass

What is the ideal gas equation

PV = nRT
where,
P → pressure
V → Volume
n → Number of moles

R → Universal gas constant

T → Temperature

What are the formulae for work done in an isothermal process? Why is it so?

∆W = nRT*ln(V₂/V₁) → ∆W = 2.303*nRT*log₁₀(V₂/V₁)

And using Boyle’s Law, P ∝ 1/V

∆W = nRT*ln(P₁/P₂) → ∆W = 2.303*nRT*log₁₀(P₁/P₂)

The reason we are doing this is that pressure isn’t constant and is rather variable

What is the formula for the fraction of heat used to increase internal energy in an isobaric process?

∆U/∆Q = 1/γ

What is the formula for the fraction of heat used to increase the work done in an isobaric process?

∆W/∆Q = 1- 1/γ

What is the ideal gas equation for adiabatic processes

PV^γ = nRT

What is the formula for work done in an adiabatic process

∆W = nR∆T/1-γ

What is an adiabatic wall

It is a type of wall where there is no heat flow between 2 objects

What is a diathermal wall

It is a type of wall where there is heat flow between 2 objects

What is the ideal gas equation for polytropic processes

PV^x = nRT

What is the work done in Polytropic process

∆W = nR∆T/1-x

What are the 2 formulae for Molar heat capacity in polytropic processes

1. C_m = C_v + R/1-x

2. C_m = R/1-γ + R/1-x

What are the main points in the Kinetic theory for gases

1. Molecules considered are large in number

2. No energy lost

3. Collisions are elastic

4. The distance between the molecules is > size of the molecules

5. Momentum is conserved

When is the Kinetic theory for gases valid for ideal gas

At high temperature and low pressure

What is the value of the universal gas constant in

1. SI unit

2. CGS unit

1. 8.31 J/Kelvin mol (or) 25/3 J/Kelvin mol

2. 2 calorie/kelvin mol

When does a real gas become an ideal gas

At high temperatures

What is the formula for density of a gas

Mo → Also known as Gram molecular weight

What is the formula for the pressure of an ideal gas in a container

1/3 nmv²_rms

Where,

n → number of molecules per unit volume => N/V

m → Mass of 1 molecule

v → rms velocity

What is the formula for average velocity of a gas molecule present inside a container

√8RT/⊼*G.M.M

What is the formula for the Maximum Pivotal velocity of a gas molecule present inside a container

√2*R*T/G.M.M

What are the formula for the rms velocity of a gas molecule present inside a container

1. √PV/G.M.M

2. √3RT/G.M.M

Where,

What does the Boltzmann distribution curve tell us, and what is it?

It is a graphical representation of molecules in a container, having a number of molecules on the y-axis and velocity on the x-axis

The area of the graph gives us the number of molecules and does not depend on temperature, and the peak of the graph provides us with the velocity of the molecules, corresponding to which there is a larger number of molecules

As you increase the temp, the graph extends; Literally

What is the Mean free path? What are its formula?

It is the distance between 2 colliding objects after a collision

1. S = v*t

2. 1/ √2 ⊼ n*d²

   Where,

   n → Number density → Number of molecules/ volume

   d → Diameter of the molecule

Whenever we write density, what do we do to the formulae

We divide the formula by volume

What is free expansion

The sudden expansion of gas into a vacuum, where,

1. ∆U = 0

2. ∆Q = 0

3. ∆W = 0

4. The number of moles is always constant

What is the formula for the efficiency of the work done by a heat engine

Output/input => W/Q₁

What does gamma show in an adiabatic process

It shows the compressibility of the gas under constant pressure and volume