CBSE Class 11 Physics Notes : Thermodynamics

1. Introduction

• Thermodynamics is that branch of physics which is concerned with transformation of heat into mechanical work.
• It deals with the concepts of heat, temperature and interconversion of heat into other forms of energy i.e., electrical, mechnical, chemical magnetic etc.
• Thermodynamics does not take any account of atomic or molecular constitution of matter and it deals with the bulk systems.
• State of any thermodynamic system can be described in terms of certain know macroscopic variables known as thermodynamic variables. 
• Thermodynamic variables determine the thermodynamic behaviour of a system . Quantities like pressure(P), volume(V), and temperature(T) are thermodynamic variables. Some other thermodynamic variables are entropy, internal energy etc. described in terms of P, V and T 
• A thermodynamic system is said to be in thermal equilibrium if all parts of it are at same temperature.
• Thus two systems are said to be in thermal equilibrium if they are at same temperature.

2. Concept of Heat

• Heat may be defined as energy in transit.
• Word heat is used only if there is a transfer of energy from one thermodynamic system to the another.
• When two systems at different temperatures are kept in contect with each other then after some time temperatures of both the syatems become equal and this phenomenon can be described by saying that energy has flown from one system to another.
• This flow of energy from one system to another on account of temperature difference is called heat transfer.
• Flow of heat is a non-mechanical mode of energy transfer.
• Heat flow depends not only on initial and find states but also on path it's.

3. P-V Indicator Digram

• Only two thermodynamic variables are sufficient to describe a system because third vaiable can be calculated from equation of state of the system.
• P-V Indicator Digram is just a graph between pressure and volume of a system undergoing an operation.
• When a system undergoes an expansion from state A (P₁ V₁) to a state B (P₂V₂) its indicator digram is shown as follows.
   
• In case of compression system at state A(P₁ V₁) goes to a state B(P₂V₂) its indicator digram is as follows.
  
   
• Intermediate states of system are represented by points on the curve.
• The pressure volume curve for a fixed temperature is called isotherm.

4. Work in volume changes

• Consider a cylinder filled with gas and equiped with a movable piston as shown in fig below
  
   
  fig - Force exerted by a system during small expansion.
  Suppose,
       A - Cross Sectional area of cylinder
       P - Pressure exerted by piston at the piston face.
       PA - Force exerted by the system.
• If piston moves out by a distance dx then work done by this force is dW given by
            dW = PAdx
             = PdV                    (1)          
  since V = Adx and dV is change in volume of the system.
• In a finite volume change from V₁ to V₂
       W=∫PdV                         (2)
  where limits of integration goes from V₁ to V₂
  Graphically this relationship is shown below
  
   
• Thus eqn (2) can be interpreted graphically as area under the curve between limits V₁and V₂.
• If pressure remains constant while the volume changes, then work is
       W = P(V₂-V₁)          (3)
• Work done not only depends on initial and final states but also on the intermediate states i.e., on the path.

Learning:Work done in a process is given by area under the process on the PV diagram

5. Internal Energy and first law of thermodynamics

• Internal energy can be described as the sum of kinetic and potantial energies of individual movecules in the material.
• But in thermodynamics one should keep in mind that U is simply a macrosopic variable of the system.
• U is thermodynamic state variable and its value depends only on the given state of the system and not on path taken to arrive the state.
• Transfer of heat and performance of work are two mean of adding or subtracting energy from a system.
• On transfer of energy, system is said to have undergone a change in internal energy.
• Thus the sum of heat put into the system plus work done on the system equals increase in internal energy of the system for any process.
  if, U₁ is internal energy of state 1 and U₂ is internal energy of state 2 than change in internal energy would be
        ΔU=U₂ - U₁
• If W is the work done by the system on its surroundings then -W would be the work done on the system by the surroundings .
• If Q is the heat put into the system then,
       Q+(-W)=ΔU
  usually written as
       Q=ΔU+W                     (4)
• Equation (4) is then know as first law of thermodynamics and it can be applied when
        Q, W and U are expressed in same units.
  Some Imp stuff      (1) Q is positive when heat is given to the system and Q is negative when heat is taken from the system
       (2) W is positive when system expands and does work on surroundings
• Hence we may say that when a certain amount of heat Q is given to the system then some part of it is used in increasing internal energy ΔU of the system while remaining part leaves the system in form of work done by the system on its surroundings.
• From equation 4 we see that first law of thermodynamics is a statement of conservation of energy stated as
  ' The energy put into the system equals the sum of the work done by the system and the change in internal energy of the system'
• If the system undergoes any process in which ΔU=0 i.e., charge in internal energy is zero then from (4)
       Q = W
  that is heat supplied to the system is used up enterely in doing work on the surroundings.

6. Specific heat capacity of an ideal gas

• We have defined specific heat capacity and molar specific heat capacity earlier in the previous chapter.
• There are two specific heats of ideal gases.
  (i) Specific heat capacity at constant volume
  (ii) Specific heat capacity at constant pressure
  C_p and C_v are molar specific heat capacities of ideal gas at constant pressure and volume respectively for C_p and C_v of ideal gas there is a simple relation.
       Cp-Cv = R                         (7)
  where R- universal gascontant
• This relation can be proved as follows.
  from first law of thermaodynamics for 1 mole of gas we have
       ΔQ =Δ U+PΔV                    (8)
• If heat is absorbed at constant volume then ΔV = 0 and
        C_V=(ΔQ/ΔT)_V=(ΔU/ΔT)_V     (9)
  If Q in absorbed at constant pressure than
       C_P=(ΔQ/ΔT)_P=(ΔU/ΔT)_P+P(ΔV/ΔT)_P
  now ideal gas equation for 1 mole of gas is
       PV = RT
        = P(ΔV/ΔT) = R                    (10)
  from (9) and (10)
       C_P - C_V=(ΔU/ΔT)_P-(ΔU/ΔT)_V+P(ΔV/ΔT)_P
• Since internal energy U of ideal gas depands only on temperature so subscripts P and V have no meaning.
  =>          C_P - C_V = R
  which is the desired relation

           

CBSE Class 11 Physics Notes : Thermodynamics part 2

                                                                                                               

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