Thermodynamics PDF

THERMODYNAMICS Chapter 12 THERMODYNAMICS Thermodynamics: It is the branch of physics that deals with the concepts of heat and temperature and the inter conversion of heat and other forms of energy. In thermodynamics, the main focus is on the macroscopic quantities of the...

THERMODYNAMICS Chapter 12 THERMODYNAMICS Thermodynamics: It is the branch of physics that deals with the concepts of heat and temperature and the inter conversion of heat and other forms of energy. In thermodynamics, the main focus is on the macroscopic quantities of the system such as pressure, volume, temperature, internal energy, entropy, enthalpy etc. Thus, thermodynamics provide macroscopic description of the system. Thermodynamic system: A collection of an extremely large number of atoms or molecules confined within certain boundaries such that it has certain values of pressure, volume and temperature is called thermodynamic system. The system may be in the form of a solid, liquid, gas or a combination of two or more. Surroundings: Anything outside the thermodynamic system to which energy or matter is exchanged is called its surroundings. A system may be divided into three groups (types);  Open system: It can exchange both energy and matter with its surroundings.  Closed system: It can exchange only energy with its surroundings.  Isolated system: It will not exchange both energy and matter with its surroundings. Adiabatic wall: A wall which does not allow any exchange of energy between the systems is known as adiabatic wall. Diathermic wall: A wall which allows any exchange of energy between the systems is known as adiabatic wall. Thermodynamic state variables (State variables): Variables which are required to specify the state of thermodynamic system are called thermodynamic state variables. Ex: Pressure, Temperature, Volume, Mass, Composition, Internal energy etc. Equation of state: The equation which relates the state variables is called equation of state. The equation of state for an ideal gas is, Types of thermodynamic state variables: State variables are of two types, (i) Extensive thermodynamic state variable, (ii) Intensive thermodynamic state variable Extensive thermodynamic state variables: The variables whose value changes for each part of the system are called Extensive thermodynamic state variables. Ex: Internal energy, volume and mass. Intensive thermodynamic state variables: The variables whose value remains unchanged for each part of the system are called intensive thermodynamic state variables. Ex: Temperature, pressure and density. Note: Extensive state variables depend on the size of the system but intensive state variables do not. Page | 1  THERMODYNAMICS Thermal equilibrium: Two systems in contact are said to be in thermal equilibrium, if both are at the same temperature. In thermal equilibrium, thermodynamic variables such as pressure, volume, temperature, mass and composition will not change with time, for a closed system. That is the system has mechanical, thermal and chemical equilibrium. Zeroth law of thermodynamics: When two systems and are separately in thermal equilibrium with a third system , then the two systems and are also in thermal equilibrium with each other. Zeroth law was formulated by R H Flower. Significance of Zeroth law: Significance of this law is, all the systems in thermal equilibrium with one another must have a common physical quantity that has the same value for both, called temperature. Heat: Energy that is transferred between a system and its surroundings whenever there is a temperature difference between the system and surroundings is called heat. When energy is transferred to the system from its surroundings, then heat is taken as positive. When energy is transferred to the surroundings from the system, then heat is taken as negative. Work done: Work is said to be done, if a system moves through a certain distance in the direction of the applied force. Expression for work done by the system: Let a gas taken in the cylinder. Let the cylinder is fitted with a frictionless piston of area of cross-section. Let be the pressure of the gas on the cylinder. The force on the piston, Let the piston be displaced through a distance during the expansion of the gas. Work done by the gas, ∫ ∫ Sign convention: (i) When a system expands against the external pressure, ( ) is positive. Hence work done by the system and is taken as positive. (ii) When a system is compressed, is negative. Hence work done on the system and is taken as negative. Internal energy: The sum of kinetic and potential energy of the constituent particles of the system is known as internal energy. It is denoted by. Page | 2  THERMODYNAMICS Note: In the case of an ideal gas we assume that intermolecular forces are zero. Thus. Hence the internal energy is purely kinetic energy and depends only on temperature. In real gases, intermolecular forces are not zero, Sign Convention: (i) Increase in internal energy is taken as positive and (ii) Decrease in internal energy is taken as negative. Note: Heat and work are not state variables. They are modes of energy transfer to a system resulting in change in its internal energy. First law of thermodynamics: When some quantity of heat is supplied to a system, then the quantity of heat absorbed by the system is equal to the sum of the increases in the internal energy of the system and the external work done by the system against the expansion. Mathematically, or Significance of first law: First law of thermodynamics is law of conservation of energy. Specific heat capacities (Mayer’s relation): From first law of thermodynamics, For one mole of gas, If is the heat absorbed at constant volume, then That is, ( ) ( ) Where the subscript V is dropped in the last step, since U of an ideal gas depends only on temperature. If is the heat absorbed at constant pressure, then ( ) ( ) ( ) ( ) The subscript P is dropped in the first tem, since U of an ideal gas depends only on temperature. Now, for a mole of an ideal gas, ( ) Using the equations (1) and (3) in (2), We have, Thermodynamic process: Any process in which the thermodynamic variables of a system change is known as thermodynamic process. Page | 3  THERMODYNAMICS Quasi-static process: A process in which the system departs only infinitesimally from the equilibrium state is known as quasi-static process. In this process, the change in pressure or change in volume or change in temperature of the system is very, very small. Note: Non-equilibrium states of a system are difficult to deal with. It is, therefore, convenient to imagine an ideal process in which at every stage the system is an equilibrium state. Such a process is infinitesimally slow, hence the name quasi-static. Isothermal process: A process in which the temperature of the system is kept constant throughout is called an isothermal process. In this case and change, but As the temperature is constant, no change in internal energy,. From first law of thermodynamics, or Heat supplied in an isothermal process is used to do work against the surrounding. Ex: Boiling of a liquid, melting of wax or ice etc. Expression for Work done during an Isothermal process: Consider an ideal gas which changes its state from to at constant temperature. ∫ ∫ ∫ ∫ [ ] [ ] Note: (i) If then. (ii) If then. Isotherm: The pressure-volume curve for a fixed temperature is called an isotherm. Adiabatic process: The process in which heat energy neither enters nor leaves the system is called adiabatic process. In this case, and change, but. From first law of thermodynamics, When gas expands adiabatically, is positive. Therefore must be negative. That is internal energy of the system decreases. Ex: Bursting of an automobile tube inflated with air, propagation of sound waves in a gas. Page | 4  THERMODYNAMICS Expression for work done during an adiabatic process: Let a gas in state be adiabatically expand to the state ∫ For an adiabatic process, ∫ [ ] * + * + * + [ ] [ ] ( ) ( ) Note: (i) If , Temperature decreases when the gas expands. (ii) If , Temperature increases when the gas compressed. Isochoric process: A thermodynamic process that takes place at constant volume is called isochoric process. As the volume is kept constant, From first law of thermodynamics, If heat is absorbed by a system at constant volume, its internal energy increases. Ex: Melting of a solid into liquid. Isobaric process: A thermodynamic process that takes place at constant pressure is called isobaric process. Work done by the gas is, ( ) ( ) Ex: Heating any liquid at atmospheric pressure, heating a gas at constant pressure. Cyclic process: It is the process in which the system returns to its initial state after a number of changes. In cyclic process, change in internal energy is zero. From the first law of thermodynamics, Net work done during a cyclic process must be equal to the amount of heat energy transferred. Page | 5  THERMODYNAMICS Reversible process: It is a process which can be made to proceed in the opposite direction with same ease so that the system and the surroundings pass through exactly the same intermediate state as in the direct process. Ex: Conversion of ice to water and vice versa, under ideal conditions. Irreversible process: A process in which the system cannot be retraced to its original state is called an irreversible process. Ex: A body moving on a rough surface from one point to another. Page | 6  THERMODYNAMICS Second law of thermodynamics: This law specifies the condition of transformation of heat into work. Kelvin-Planck statement: No process is possible whose only result is the absorption of heat from a reservoir and the complete conversion of heat into work. Clausius statement: No process is possible whose only result is the transfer of heat from a colder object into a hotter object. Carnot engine: Sadi Carnot introduced the concept of an ideal heat engine called Carnot engine. Construction: Parts of the Carnot engine are,  Source: It is maintained at a fixed higher temperature  Sink: It is maintained at fixed low temperature than the source.  Working substance: A perfect gas acts as working substance. The container is fitted with a piston which can slide without friction and it is also non-conducting. Container has conducting base and non-conducting side wall.  Insulated stand: It is used to provide complete thermal isolation for working substance that can undergo adiabatic operation. Carnot cycle: The working substance of the Carnot engine is taken through a cycle of isothermal and adiabatic process known as Carnot cycle. Carnot cycle for a heat engine with an ideal gas as the working substance is as shown. Steps of Carnot cycle: Step1- Isothermal expansion: The cylinder with gas having pressure , volume and temperature is kept on the source at temperature. The gas is allowed to expand isothermally slowly. The temperature tends to decrease, but it is maintained at constant temperature by absorbing heat from source. Let the pressure and volume change to and respectively. For an isothermal process, Page | 7  THERMODYNAMICS ( ) Step2-Adiabatic expansion: The cylinder is placed on the non-conducting stand and the gas is allowed to expand adiabatically until the temperature falls to. To make the gas recover its capacity for doing work, it should be brought to the original condition. This is done in next steps. Step3-Isothermal compression: The cylinder is kept on sink at temperature. The gas is compressed isothermally. Let amount of heat is rejected to the sink. Let the pressure and volume change to and respectively. For an isothermal process, ( ) sign indicates work is done on the system. ( ) Step4-Adiabatic Compression: The cylinder is placed on the non-conducting stand and the gas is compressed adiabatically till the pressure , volume changes to and and temperature. Total work done during the complete cycle is, Since , Note: Work done, Efficiency of Carnot engine: ( ) ( ) ( ) ( ) For the step2, we have adiabatic equation, For Step4, we have adiabatic equation, Page | 8  THERMODYNAMICS ( ) ( ) ( ) ( ) Note:  Efficiency of Carnot engine depends upon the temperature of the source and sink.  Efficiency is independent of the nature of the working substance.  Since we cannot have a sink at absolute zero, so a heat engine with 100% efficiency is not possible to realise in practice. Page | 9  THERMODYNAMICS Suggested Questions. One Mark. 1) What is equation of state for adiabatic process? 2) Name the factor on which internal energy of a gas depends. 3) State the Zeroth law of thermodynamics. 4) What is the significance of zeroth law of thermodynamics? 5) State the first law of thermodynamics. 6) Mention the significance of I law of thermodynamics. 7) What is Quasi-static process? 8) Which physical quantity is conserved for an iso-thermal process? Two Marks. 1) What are Diathermic and adiabatic wall? 2) What are state variables? Give two examples. 3) Mention the an example for isothermal and adiabatic process each. 4) Mention the quantities remaining constant during isobaric and isochoric processes. Five Marks. 1) Discuss the applications of first law of Thermodynamics. 2) What is isothermal process? Derive the expression for work done in isothermal process. 3) Explain different stages of Carnot’s cycle with P-V diagram. or Explain Carnot’s Cycle 4) Draw a schematic diagram of pressure versus volume for a Carnot cycle with an ideal gas as working substance. Write an expression for efficiency of a Carnot engine. 1.. Numerical Problems. 1. A Carnot engine has an efficiency of 0.3, when the temperature of the sink is 350K. Find the change in temperature of the source when the efficiency becomes 0.5. 3. A steam engine delivers 7.5×108 J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute? Also find the ratio of temperature of sink to the source. Page | 10