Here students can locate TS Inter 1st Year Physics Notes 13th Lesson Thermodynamics to prepare for their exam.

## TS Inter 1st Year Physics Notes 13th Lesson Thermodynamics

→ Thermodynamics: It is a branch of physics in which we shall study the process where work is converted into heat and vice versa.

→ Thermodynamic variables: In thermodynamics the state of a gas is specified by macroscopic variables such as pressure, temperature, volume, mass and composition that are felt by our sense perceptions and are measurable.

→ Thermal equilibrium: In general at thermal equilibrium the temperatures of the two bodies or systems are equal.

In a thermally isolated system it is said to be in “thermal equilibrium” if the thermodynamic variables such as pressure, volume, temperature, mass and composition do not change with time and they have fixed values.

→ Zeroth law of thermodynamics: It states that if two systems say A & B are in thermal equilibrium with a third system ‘C’ separately then the two systems A and B are also in thermal equilibrium with each other.

→ Internal energy: It includes only the energy associated with random motion of molecules of the system

i. e., internal energy is simply the sum of kinetic and potential energies of these molecules. Internal energy is denoted by ‘U’.

→ First law of thermodynamics: The heat energy (dQ) supplied to a system is partly used to increase its internal energy (dU) and the rest is used to do work (dW)

i. e., dQ = dU + dW. (OR)

Heat energy supplied to a system (dQ) always equals to the sum of change in internal energy (dU) and workdone (dW).

This law is a consequence of ”law of conservation of energy.”

→ Isothermal expansion: If a system is taken through a thermodynamic process in which ΔU = 0 then it is called Isothermal process.

In isothermal process change in internal energy ΔU = 0 i.e., temperature of the system is constant. Isothermal process obeys gas equation PV = RT.

→ Adiabatic process: In an adiabatic process system is insulated from the surroundings. So energy absorbed or released is zero (ΔQ = 0). In adiabatic process temperature of the system may change. It follows the equation PV^{γ} = constant. Where γ = \(\frac{C_P}{C_V}\) ratio of specific heats of a gas.

→ Isobaric process: In isobaric process pressure P’ is kept constant, volume and temperature changes are permitted. Work done in isobaric process

W = P(V_{2} – V_{1}) = µR(T_{2} – T_{1}).

→ Isochoric process: In isochoric process volume (V) of the system is kept constant. Work done by isochoric process is zero. In this process heat energy absorbed is totally used to increase the internal energy of the system.

→ Cyclic process: In a cyclic process the system returns to initial state (P, V and T). Change in internal energy ΔU = 0. Heat absorbed during cyclic process is equal to work done.

→ Reversible process : A thermodynamic process is said to be reversible if the process can be turned back such that both the system and surroundings return to their original state, with no other change any where else in universe.

→ Irreversible process : If a thermodynamic process cannot be reversed exactly in opposite direction of direct process then it is called irreversible process.

All spontaneous process of nature are irreversible.

→ Quasi static process: In a quasi static process at every stage the difference on pressure and temperature of systems and surroundings is infinitesimally small.

i.e., P + ΔV ≈ P and T + ΔT = T .

In this process the thermodynamic variables (P,V,T) will change very slowly so that it remains in thermal and mechanical equilibrium with surroundings throughout that process.

Note: Quasi static process is an imaginary concept only.

→ Heat engines: A heat engine is a device by which a system is made to undergo a cyclic process. As a result heat is converted into work.

Work done by heat engine W= Q_{1} – Q_{2};

Work done by heat engine W= Q1 — Q2; efficiency η = 1 – \(\frac{\mathrm{Q}_2}{\mathrm{Q}_1}\) (or) η = 1 – \(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\)

Important parts of heat engine : every heat engine mainly consists of

- hot source,
- working substance,
- cold reservoir.

→ Refrigerators or heat pumps : A Refrigerator is a heat pump which is a reverse of heat engine. Here working substance extracts heat Q_{2} from cold body at temperature T_{2} and delivers it to hot reservoir at temperature T_{1}. Coefficient of performance of refrigerator

α = \(\frac{\mathrm{Q}_2}{\mathrm{~W}}=\frac{\mathrm{Q}_2}{\mathrm{Q}_1-\mathrm{Q}_2}\)

→ Second law of thermodynamics :

(a) Kelvin – Planck statement: No process is possible whose sole resultant is the absor-ption of heat from a reservoir and the complete conversion of heat into work.

(b) Clausius statement: No process is possible whose sole resultant is the transfer of heat from a colder object to a hotter object.

Second law of thermodynamics gives a fundamental limitation to the efficiency of heat engine i.e. heat released to a colder body will never become zero. So 100% efficiency of heat engine cannot be achieved.

→ Carnot engine : Carnot engine operates between a hot reservoir of temperature T_{1} and a coldreservoir of temperature T_{2} through a cyclic process.

This cyclic process consists of

- Iso-thermal expansion,
- Adiabatic expansion,
- Isothermal compression and
- Adiabatic compression.

In this cyclic process it absorbs heat energy from source and releases heat energy Q2 to cold reservoir efficiency of

Carnot engine η = 1 – \(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\)

→ Carnot theorem: (a) Any heat engine working between two given temperatures T_{1} and T_{2} cannot have efficiency more than that of carnot engine, (b) The efficiency of a carnot engine is independent of nature of working substance.

→ Isotherm: The pressure (p) and volume (v) curve for a given temperature is called isotherm.

→ adiabatic wall: An insulating wall that does not allow heat energy to flow from one side to another side is called “adiabatic wall.”

→ diathermic wall : It is a conducting wall which transfers heat energy from one side to another side.

→ Heat mechanical equivalent (J): In M.K.S system heat and work are measured with same unit ‘joule’. But in C.G.S system heat is measured in calorie and work in erg (1 joule = 10^{7} erg).

So in C.G.S system a conversion factor heat mechanical equivalent (J) is used to convert work into heat or vice versa.

1 Calorie = 4.2 Joules ⇒ J = 4.2 Joule/ cal. or J = 4200 joule/kilocal.

→ Calorie: The amount of heat energy required to rise the temperature of 1 gram of water through 1°C or 1 K is defined as “calorie.” Note: Magnitude of calorie slightly changes with the initial temperature of water.

→ Mean 15 °C calorie : The amount of heat energy required to rise the temperature of 1 gram of water from 14.5 °C to 15.5 °C is called “mean 15 °C calorie.”

→ Joule’s Law, work W ∝ Q ⇒ W = JQ where J = mechanical of heat equivalent

J = \(\frac{\text { Work }}{\text { Heat }}\) = 4.18 J/Cal.

→ From 1st Law of thermodynamics, dQ = dU + dW

→ Heat capacity of a body = \(\frac{\Delta \mathrm{Q}}{\Delta \mathrm{t}}\) = me (i.e., mass × specific heat)

→ Specific heat S or C = \(\frac{\Delta Q}{m \Delta t}\) = \(\frac{\text { Heat energy supplied }}{\text { mass } \times \text { temperature difference }}\)

→ From method of mixtures, Heat lost by hot body = Heat gained by cold body

→ When two spheres of radii r_{1} : r_{2} and ratio of specific heats S_{1}: S_{2} and densities p_{1}: p_{2} then their thermal capacities ratio

= \(\frac{m_1 S_1}{m_2 S_2}=\left(\frac{r_1}{r_2}\right)^3\left(\frac{\rho_1}{\rho_2}\right)\left(\frac{S_1}{S_2}\right)\)

(a) Specific heat of a gas, C_{p} = ΔQ / mΔT

(b) Molar specific heat, C_{p} = \(\frac{\Delta \mathrm{Q}}{\mathrm{n} \Delta \mathrm{t}}\) (n = Number of moles)

(c) Ratio of specific heats, y = C^{p}/ C^{v};

C^{v} = \(\frac{\mathrm{R}}{\gamma-1}\), C^{p} = \(\frac{\gamma \mathrm{R}}{\gamma-1}\)

C^{v} = \(\frac{C_V}{M}=\frac{1}{M} \frac{R}{(\gamma-1)}\)

= \(\frac{\mathrm{PV}}{\mathrm{M}(\gamma-1) \mathrm{T}} \frac{\mathrm{P}}{\rho \mathrm{T}(\gamma-1)}\)J/kg-K

or C^{v} = \(\frac{P}{\mathrm{~J} \rho \mathrm{T}(\gamma-1)}\)k.cal/kg.K

→ Work done in expanding a gas against constant pressure (P) is W = P dV.

→ Work done during ideal expansion

W = P (V_{2} – V_{1}) or W = nR (T_{2} – T_{1})

n = number of moles of gas;

R = universal gas constant.

→ Relation between C^{p} and C^{v} ⇒ C^{P} – C^{v} = R

→ Isothermal relation between P, V & T is PV = RT or PV = nRT.

→ Adiabatic relation between P, V & T

- PV
^{γ}= constant - TV
^{γ-1}= constant - PV
^{1-γ}T^{γ}= constant.

→ Work done in Isothermal process

(a) W = RT log_{e} \(\frac{V_2}{V_1}\)

(b) W = 2.303 RT log_{10} \(\frac{V_2}{V_1}\)

→ Work done in adiabatic process,

(a) W = \(\frac{1}{\gamma-1}\) (P_{1}V_{1} – P_{2}V_{2}) per mole (OR)

(b) W = \(\frac{\mathrm{nR}}{\gamma-1}\) (T_{1} – T_{2});

n = number of moles.

→ Efficiency of heat engine, η = 1 – \(\frac{\mathrm{Q}_2}{\mathrm{Q}_1}\) or η = 1 – \(\frac{\mathrm{T}_2}{\mathrm{T}_1}\)

T_{1} = Temperature of source,

T_{2} = Temperature of sink.

→ Heat energy supplied to heat a body within the same state is Q = mct.

→ Heat energy supplied during change of state is Q = mL.