TThermodynamics 647 Chapter 14 Thermodynamics Thermodynamics is a branch of science which deals with exchange of (2) Thermodynamic variables and equation of state : A thermodynamic heat energy between bodies and conversion of the heat energy into system can be described by specifying its pressure, volume, temperature, mechanical energy and vice-versa. internal energy and the number of moles. These parameters are called thermodynamic variables. The relation between the thermodynamic Some Definitions variables (P, V, T) of the system is called equation of state. For moles of an ideal gas, equation of state is PV = RT and for 1 (1) Thermodynamic system mole of an it ideal gas is PV = RT (i) It is a collection of an extremely large number of atoms or (3) Thermodynamic equilibrium : In steady state thermodynamic molecules variables are independent of time and the system is said to be in the state (ii) It is confined with in certain boundaries. of thermodynamic equilibrium. For a system to be in thermodynamic (iii) Anything outside the thermodynamic system to which energy or equilibrium, the following conditions must be fulfilled. matter is exchanged is called its surroundings. (i) Mechanical equilibrium : There is no unbalanced force between the system and its surroundings. Surrounding (ii) Thermal equilibrium : There is a uniform temperature in all parts of the system and is same as that of surrounding. (iii) Chemical equilibrium : There is a uniform chemical composition through out the system and the surrounding. (4) Thermodynamic process : The process of change of state of a Gas System system involves change of thermodynamic variables such as pressure P, volume V and temperature T of the system. The process is known as thermodynamic process. Some important processes are (i) Isothermal process : Temperature remain constant Fig. 14.1 (iv) Thermodynamic system may be of three types (ii) Adiabatic process : No transfer of heat (a) Open system : It exchange both energy and matter with the (iii) Isobaric process : Pressure remains constant surrounding. (b) Closed system : It exchange only energy (not matter) with the (iv) Isochoric (isovolumic process) : Volume remains constant surroundings. (v) Cyclic and non-cyclic process : Incyclic process Initial and final states (c) Isolated system : It exchange neither energy nor matter with the are same while in non-cyclic process these states are different. surrounding. (vi) Reversible and irreversible process : 648 Thermodynamics (5) Indicator diagram : Whenever the state of a gas (P, V, T) is (iii) Change in internal energy does not depend on the path of the changed, we say the gaseous system is undergone a thermodynamic process. process. So it is called a point function i.e. it depends only on the initial and The graphical representation of the change in state of a gas by a final states of the system, i.e. U U U thermodynamic process is called indicator diagram. Indicator diagram is f i plotted generally in pressure and volume of gas. (3) Work (W) : Suppose a gas is confined in a cylinder that has a Zeroth Law of Thermodynamics movable piston at one end. If P be the pressure of the gas in the cylinder, then force exerted by the gas on the piston of the cylinder F = PA (A = Area If systems A and B are each in thermal equilibrium with a third system of cross-section of piston) C, then A and B are in thermal equilibrium with each other. Piston Insulating Conducting System System System System A B A B dx System System F C C Gas Conducting Insulating Fig. 14.4 (A) (B) When the piston is pushed outward an infinitesimal distance dx, the (1) The zeroth law leads to theFig. 14.3concept of temperature. All bodies in work done by the gas dW F.dx P(A dx) P dV thermal equilibrium must have a common property which has the same For a finite change in volume from V to V value for all of them. This property is called the temperature. i f Vf (2) The zeroth law came to light long after the first and seconds laws Total amount of work done W P dV P(Vf Vi) Vi of thermodynamics had been discovered and numbered. It is so named because it logically precedes the first and second laws of thermodynamics. (i) If we draw indicator diagram, the area bounded by PV-graph and volume axis represents the work done Heat, Internal Energy and Work in Thermodynamics P (1) Heat (Q) : It is the energy that is transferred between a system P and its environment because of the temperature difference between them. Work = Area = P(V – V) 2 1 (i) Heat is a path dependent quantity e.g. Heat required to change the A temperature of a given gas at a constant pressure is different from that required to change the temperature of same gas through same amount at constant volume. V V2 V P 1 Fig. 14.5 (ii) For gases when heat is absorbed and temperature changes Q CT V2 P Work PdV P(V2 V1) V1 At constant pressure (Q)P CP T At constant volume (Q) C T V V V dV V V (2) Internal energy (U) : Internal energy of a system is the energy 1 2 possessed by the system due to molecular motion and molecular Fig. 14.6 P configuration. The energy due to molecular motion is called internal kinetic energy U K and that due to molecular configuration is called internal potential energy U P Work = 0 i.e. Total internal energy U UK UP (i) For an ideal gas, as there is no molecular attraction Up 0 V Fig. 14.7 i.e. internal energy of an ideal gas is totally kinetic and is given by P 3 3 P2 U UK RT and change in internal energy U R T 2 2 Work = Area of the shown trapezium (ii) In case of gases whatever be the process 1 P1 (P1 P2)(V2 V1) f R R(T T ) 2 U RT C T T f i 2 V ( 1) 1 V V2 V 1 Fig. 14.8 RT RT (P V P V ) (ii) From W PV P(V V ) f i f f i i f i 1 1 If system expands against some external force then Vf Vi W = positive TThermodynamics 649 If system contracts because of external force then Vf Vi Q = U + W W = negative (3) It makes no distinction between work and heat as according to it the internal energy (and hence temperature) of a system may be increased P B P B Negative Positive either by adding heat to it or doing work on it or both. work work (4) Q and W are the path functions but U is the point function. A A (5) In the above equation all three quantities Q, U and W must V V be expressed either in Joule or in calorie. (A) Expansion (B) Compression (6) The first law introduces the concept of internal energy. (iii) Like heat, work done is alsoFig. depends14.9 upon initial and final state of the system and path adopted for the process (7) Limitation : First law of thermodynamics does not indicate the P direction of heat transfer. It does not tell anything about the conditions, under which heat can be transformed into work and also it does not A 1 indicate as to why the whole of heat energy cannot be converted into P mechanical work continuously. A 2 B A1 V Table 14.1 : Useful sign convention in thermodynamics (A) Less area 1 B Quantity Sign Condition P V 2 + When heat is supplied to a system A Q – When heat is drawn from the system A2 B + When work done by the gas (expansion) W V – When work done on the gas (compression) A < A W < W (B) More area 1 2 1 2 (iv) In cyclic process, work doneFig is. 14.10equal to the area of closed curve. It + With temperature rise, internal energy increases U is positive if the cycle is clockwise and it is negative if the cycle is – With temperature fall, internal energy decreases anticlockwise. P C P2 Isobaric Process Work = Area of triangle ABC When a thermodynamic system undergoes a physical change in such a 1 way that its pressure remains constant, then the change is known as (V V )(P P ) A 2 2 1 2 1 isobaric process. P1 B (1) Equation of state : In this process V and T changes but P remains V1 V2 V constant. Hence Charle’s law is obeyed in this process. Fig. 14.11 P C V1 V2 P Hence if pressure remains constant V T 2 T T Work = Area of rectangle ABCD 1 2 (2) Indicator diagram : Graph 1 represent isobaric expansion, graph 2 = AB AD represent isobaric compression. A = (V – V) (P – P) P1 B 2 1 2 1 P P V1 V2 V 2 1 Fig. 14.12 P dP P2 Slope = 0 Slope = dV V V Work = (P2 P1)(V2 V1) (A) Expansion 4 (B) Compression P 1 Fig. 14.14 (i) In isobaric expansion (Heating) V1 V2 V Temperature increases so U is positive Fig. 14.13 First Law of Thermodynamics (FLOT) Volume increases so W is positive (1) It is a statement of conservation of energy in thermodynamical process. Heat flows into the system so Q is positive (ii) In isobaric compression (Cooling) (2) According to it heat given to a system (Q) is equal to the sum of increase in its internal energy (U) and the work done (W) by the system Temperature decreases so U is negative against the surroundings.