Chapter 18 Thermodynamics

Temperature and Thermometers Temperature of a system can be defined as the properly that determines whether or not the body is in thermal equilibrium with neighboring system. Temperature is an SI base quantity related to our sense of hot and cold. It is measured with a thermometer, which contains a working substance with a measurable property, such as length or pressure, that changes in a regular way as the substance becomes hotter or colder.

Thermometry The branch of heat relating to the measurement of temperature of a body is called thermometry. Types of thermometers: – Liquid Thermometer: based on principle of change in volume of liquid with change in temperature. Example mercury and alcohol thermometer. – Gas Thermometer: based on principle of changes in pressure or volume with change in temperature. Example: constant volume hydrogen thermometer. – Thermo-electric thermometers: based on the principle of thermoelectricity. E.g. Platinum and Rhodium.

– Radiation thermometers: based on the quantity of heat radiation emitted by a body e.g. furnace. This instrument is also called pyrometer. – Vapor pressure thermometer: based on the principle of change of vapor pressure with change in temperature. He- vapor pressure thermometer. – Bimetallic thermometer: based on the principle of expansion of solids. Used to measure temperatures at high altitude. – Magnetic thermometer: based on the principle of susceptibility of a substance with temperature. Used for measuring low temp near to absolute zero temperature.

Review: The susceptibility of a material or substance describes its response to an applied field.

Zeroth Law of Thermodynamics When a thermometer and some other object are placed in contact with each other, they eventually reach thermal equilibrium. The reading of the thermometer is then taken to be the temperature of the other object. The process provides consistent and useful temperature measurements because of the zero-th law of thermodynamics.

Triple point The melting point of ice decreases with increase in pressure. It means that ice melts at a temperature lower that 0 degree C at a pressure higher than the normal pressure. The curve AB represents the relation between pressure(P) and temperature(T). The curve AB is called ice line. The substance will exist in the solid state (ice) to the left of the AB curve and in the liquid state to the right of the AB curve. AB curve represents the equilibrium state between liquid and solid.

The boiling point of water increases with increases in P. The curve CD represents the relation between P and T and it is called the steam line. Above the CD curve substance is in the liquid state and below the CD curve it is the vapor state. The CD curve represents the equilibrium between the liquid and vapor states

The curve EF represents the equilibrium between the solid and the vapor states of a substance and is called the Hoar-frost line. Above the EF the substance is in the solid state and below the EF the substance is in the vapor state. The there curve meet at a point O. it is called triple point.

Triple-point temperature

Thermodynamic variables and equation of state The thermodynamic state or macroscopic state of a system can be determined by the 4 properties (composition, P, V, T). These are called the state variable. For a homogeneous system composition is same. The state of the system is determined by P,V,T. For a system the equation of state can be written as These are not independent variables, if we know 2 of them then we can calculate the third one. Example

Classes of system Open system: It can exchange matter and energy with the surroundings. Example: Air compressor. Closed system: It can exchange only energy with the surroundings. Example: Gas enclosed in a cylinder. Isolated system: A system which is thermally insulated and has no communication of heat or work with the surrounding.

Thermodynamic Equilibrium A system in thermodynamic equilibrium must satisfy the following requirements strictly: Mechanical Equilibrium: No macroscopic movement (Net force=0) with in the system. Thermal Equilibrium:, between the parts of system and between system and surrounding. Chemical Equilibrium: No chemical reaction with in the system and no movement of chemical constituent.

Internal Energy Internal Energy: – the energy content of a system. – Sum of kinetic energy (due to translational, rotational and vibrational motion of molecules which only depends on T) and potential energy (due to intermolecular force)

Heat Heat is the energy transferred between a system and its environment because of a temperature difference that exist between them

Law of Fusion Every substance changes its state from solid to liquid at a particular temperature under normal pressure called the melting point. As long as the change of state takes place there is no change in temperature. One gram of every substance requires a definite quantity of heat for change of state from solid to liquid and it is called the latent heat of fusion. It is different for different substance. The melting point of those substances which decrease in volume on melting. I lowered with increase in pressure.

Heat- A path function Path function and Point function are introduced to identify the variables of thermodynamics. Path function: Their magnitudes depend on the path followed during a process as well as the end states. – Work (W), heat (Q) are path functions. Process A: W A = 10 kJ Process b: W B = 7 kJ Point Function: They depend on the state only, and not on how a system reaches that state. All properties are point functions. – Process A: V 2 - V 1 = 3 m 3 Process B: V 2 - V 1 = 3 m 3

Work-A path function Let a system is taken from an initial equilibrium state 1 to a final equilibrium state 2 by two different path A and B. The process is quasistatic. For the path A For the path B

Heat and work are path function. They depend on the process. They are not point functions such as pressure or temperature

Modes of heat transfer The three modes of heat transfer always exist simultaneously. For example, the heat transfer associated with double pane windows are: Conduction: Hotter (cooler) air outside each pane causes conduction through solid glass. Convection: Air between the panes carries heat from hotter pane to cooler pane. Radiation: Sunlight radiation passes through glass to be absorbed on other side.

Convection Heat transfer between a solid surface and an adjacent gas or liquid. It is the combination of conduction and flow motion. Heat transferred from a solid surface to a liquid adjacent is conduction. And then heat is brought away by the flow motion. Newton's law of cooling: h = Convection heat transfer coefficient; T s = Temperature of the solid surface T f = Temperature of the fluid

The atmospheric air motion is a case of convection. In winter, heat conducted from deep ground to the surface by conduction. The motion of air brings the heat from the ground surface to the high air.

Radiation The energy emitted by matter in the form of electromagnetic waves as a result of the changes in the electronic configurations of the atoms or molecules. Stefan - Boltzmann law: σ = Stefan - Boltzmann constant ε = emissivity T s = Surface temperature of the object Solar energy applications mainly use radiation energy from the Sun.

Newton’s law of cooling Statement: the rate of loss of heat of a body is directly proportional to the difference of temperature of the body and surroundings. Characteristics: The law holds good only for small difference of temperature Mathematically Body mass Temperature of surrounding Specific heat

Problem A liquid takes 5 mins to cool from 80 to 50 deg-C. How much time will it take to cool from 60 to 30 deg-C. The ambient temp=20 degC Here

Home work A liquid takes 4 mins to cool from 70 to 50 deg-C. How much time will it take to cool from 50 to 40 deg-C. The ambient temp=25 degC – Answer: 3.418min

Example When a system is taken from the state A to the state B alone the path ACB, 80 J of heat flows into the system and the system does 30J of work. – How much heat flows into the system alone the path ADB, if the work done is 10 J. – The system is returned form the state B to the state A along the curved path. The work done on the system is 20 J Does the system absorb or liberate heat and how much? – If U A =0 U D =40 J. Find the heat absorbed in the process AD and DB

Along ACB – H ACB =U B -U A +W; 80=U B -U A +30; U B -U A =50 J Along ADB – H ADB =U B -U A +W=50+10=60 J Path B to A: H=U A -U B +W=-50-20=-70 J H ACB =80 W=30

U A =0 U B -U A =50 J. U B =50J. In the process ADB 10 J of work is done. From A to D is 10 J and D to B is 0J. For AD: H AD =U D -U A +W=40+10=50J; For DB: H DB =U B -U D +W= =10J;

Remember Isothermal: Temperature remains constant throughout the process. Adiabatic: The working substance is perfectly insulated from the surroundings. It can never give heat nor take heat from surroundings. When work is done on the working substance, there is rise in temperature because the external work done on the working substance increases its internal energy. Isochoric: If the working substance is taken in a non expanding chamber the heat supplied will increase the P and T. V is constant.

Isobaric: if the working substance is taken in an expanding chamber kept at a constant pressure, the process is called an isobaric process. Here the T and V will change.