# Nootan Solutions Isothermal and Adiabatic Processes ISC Class-11 Physics Nageen Prakashan

Nootan Solutions Isothermal and Adiabatic Processes ISC Class-11 Physics Nageen Prakashan Chapter-20. Numericals of latest edition. Step by step Solutions of Kumar and Mittal ISC Physics Part-2 Class-11 Nageen Prakashan Numericals Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Physics.

## Nootan Solutions Isothermal and Adiabatic Processes  ISC Class-11 Physics Nageen Prakashan

 Class: 11 Subject: Physics Part-2 Chapter 20     Isothermal and Adiabatic Processes
 Board ISC Writer / Publications Nootan / Nageen Prakashan / Kumar and Mittal Topics Solved Numericals of page 779, 780

### Nootan Solutions Isothermal and Adiabatic Processes  ISC Class-11 Physics Nageen Prakashan

#### Adiabatic Processes :-

• Adiabatic is a process in which there is no heat flow takes place between the system and the surroundings.
• These processes are sudden.
• The walls of the container should be adiabatic
• For an adiabatic process of an ideal gas
• From Boyle’s law
• PV γ = constant

Where γ = Cp/Cv Specific heat ratio

Example: – Hot tea in Thermos flask. It will remain hot as there is no exchange of heat takes place because the walls of thermos is insulating.

#### Adiabatic change of an ideal gas :-

• It implies how much work is done during adiabatic change of an ideal gas.
• Initially ideal gas is at Pressure P1, Volume Vand Temperature T1 (P1,V1,T1)
• Final state of an ideal gas Pressure P2,Volume V2 and Temperature T2 (P2,V2,T2)
• P V γ = const
• γ =Cp/Cv
• If an ideal gas undergoes a change in its state adiabatically from (P1, V1) to (P2, V2)
• P1V1 γ = P2V2 γ
• The work done in an adiabatic change of an ideal gas from the

state (P1, V1, T1) to the state (P2, V2, T2).

W =∫ P V dV = P ∫V dV (Integrating between the limits V2 and V1)

For Adiabatic Process

• P V γ = constant This implies  P= constant / V γ
• W = constant ∫dV/ V γ
• constant [V γ-1/- γ+1]
• constant/1- γ [V21- γ – V1 1-γ]
• = constant/1- γ[1/ V21- γ– 1/ V1 1-γ]
• By solving Work done W= R/ (γ-1)(T2-T1), where
• T2= final Temperature
• T1=initial temperature
• R=Universal gas constant
• γ = Specific heat ratio
• This is the work done during adiabatic change.
• Consider W= R/ (γ-1)(T2-T1)

#### Isothermal Processes :-

• Isothermal :- Iso means same and thermal related to temperature. In Isothermal process the temperature remains constant throughout while all other variables change.
• Temperature is constant throughout.
• For an ideal gas
• PV = nRT where
• n=no. of moles (constant), R = universal gas constant, T =constant for isothermal process.
• This implies PV=constant
• Pressure and volume are inversely proportional to each other.
• Graphically if we plot pressure and volume

• We will get decreasing curve because if we increase pressure volume decreases and vice versa.
• This curve is known as Isothermal Curve.

#### Isothermal Expansion of an Ideal gas :-

• It can be described as amount of work done during isothermal expansion of an ideal gas under constant temperature.
• Initially ideal gas is at Pressure P1 and Volume V.
• At constant temperature the gas will expand from pressure P1 to P2 and volume changes from V1 to V2.So the final state (P2,V2).
• These all expansions are QuasiStatic processes.
• Consider any intermediate stage ,
• Pressure is P and volume is V1 + ΔV where ΔV increase in volume.
• ΔW=P ΔV where ΔW = small work done
• By solving and doing calculation the above equation the work done for an ideal gas the work done will be given as :-

W= RT lnV2/V1

### Chapter-20

Nootan Solutions Isothermal and Adiabatic Processes  ISC Class-11 Physics Nageen Prakashan

Page No 779, 780

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