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MAJOR-PHYSICS COURSE
Semester IV
MAJOR-IV: PHYS4011: Heat and Thermodynamics (Credits: Theory-04, Practicals-01)
F.M. = 75 (Theory-40, Practical–20, Internal Assessment–15)
MAJOR-IV: PHYS4011: Heat and Thermodynamics
Practical: 30 Hours
List of Experiments
1. To determine the coefficient of thermal conductivity of copper using Searle’s apparatus.
2. To determine the coefficient of thermal conductivity of a bad conductor by Lee and Charlton’s disc method.
3. Determination of the value of the Stefan’s constant.
4. To study the variation of thermo-emf across two junctions of a thermocouple with temperature.
5. To determine the temperature coefficient of resistance and the boiling point of a given liquid using Platinum resistance thermometer
6. To calibrate a thermocouple for measuring the temperature in a specified range using i) null method, ii) direct measurement using OP AMP difference amplifiers
7. To determine the coefficient of thermal expansion of a metallic rod using an optical lever
8. To determine the temperature coefficient of resistance using the Carry Foster bridge
9. To determine the coefficient of thermal expansion of a metallic rod using travelling microscope
10. To determine the pressure coefficient of air by constant volume method
MAJOR-PHYSICS COURSE
Semester IV
MAJOR-IV: PHYS4011: Heat and Thermodynamics (Credits: Theory-04, Practicals-01)
F.M. = 75 (Theory-40, Practical–20, Internal Assessment–15)
Course Objectives: The objective of the course is to infuse ideas of thermodynamic, systems, thermodynamic variables, thermodynamic processes, and allied phenomena. It is designed to familiarize students with thermodynamic potentials, the kinetic theory of gases, and the theory of radiation.
Course Outcome: On completion of this course, the students will learn the kinetic theory of gases, the basic laws of thermodynamics, the applications of the well-known Maxwell’s relations, the underlying Physics behind the Joule Thompson effect and the spectral distribution of the blackbody radiation.
The Kinetic Theory of Gases
Unit 1 Objective of the theory (Knowledge of a macroscopic system from its microscopic constituents), Classical ideal gas and the ideal gas law, A microscopic view of an ideal gas and the basic postulates of the kinetic theory, The justifications and implications of the postulates, Mean free path, Collision probability, Estimates of mean free path, The kinetic interpretation of pressure P, Relation between pressure and translational kinetic energy of the molecules, Kinetic interpretation of temperature - the average molecular kinetic energy is proportional to the absolute temperature.
Unit 2 The equipartition theorem (statement only), Kinetic degrees of freedom (f), Thermal energy and specific heat of gases (Cp and Cv), $\gamma$ - the ratio of Cp and Cv, Relation between \gamma and f, Specific heat of a monatomic, a diatomic gas (N2) gas: the experimental value and its interpretation in terms of quantum effects restricting the active modes, Brownian motion and its significance.
Unit 3 Speeds of the molecules of an ideal gas in thermal equilibrium, Maxwell–Boltzmann distribution law (statement only): Probability density ρ(c) as a function of speed c and its graphical representation, Important features of the graph and their significances: (a) Asymmetric, single peaked nature of the curve, (b) Changes in ρ(c) with (i) increasing temperature, and (ii) increasing mass of the single molecule of a gas e.g., in the cases for He, Ne, Ar, Number of molecules (𝑑𝑁) of an ideal gas moving with a speed lying between and + 𝑑 , Important conclusions: (a) Heavy molecules are unlikely to have very high speeds, (b) Number of molecules with high speeds increases with the increasing temperature, (c) Area under the curve, equal to the total number of molecules does not change with changing temperature (T), Estimation of the fraction of molecules with speeds greater than c, Average or mean speed (Cav), Root mean square velocity (Crms), Most probable speed (Cmp) from the distribution law, Comparison of Cav, Crms and Cmp at a fixed temperature (T), Maxwell-Boltzmann distribution law of molecular energies from that of the speeds, Average kinetic energy.
Unit 4 Non equilibrium state and transport phenomenon in ideal gases: (1) Viscosity: Transport of momentum, Coefficient of viscosity () in terms of the mean free path ( ), (2) Thermal conductivity: Transport of thermal energy, Thermal conductivity (K) in terms of the mean free path ( ), Effect of temperature (T) on K, (3) Diffusion: Transport of mass, Coefficient of diffusion (D) in terms of the mean free path ( ), Effect of temperature (T) and pressure on D.
Unit 5 Real gases, Andrew’s experiment on carbon dioxide: Principle, Result as isothermals (plots of the pressure versus the volume at different temperatures), Interpretation of the isothermals, Inferences from the experiment, Critical constants, Van der waals’ equation of state: Correction for finite size of the molecule, Correction for intermolecular attraction, Comparison between the nature of the isothermals obtained from Andrew’s experiment and plots of the pressure versus the volume of a gas obeying Van der waals’ equation of state at different temperatures (similarities and differences), Expression for critical constants (Tc, pc, and Vc) and critical coefficient (pcVc/RTc), Limitations of the Van der waals’ equation, Virial expansion: Concept, the Van der waals’ equation of state in terms of a virial expansion, the Boyle temperature in terms of Tc.
Heat Conduction
Thermal conductivity (K), Diffusivity (D), Fourier’s equation of heat conduction and its solution for the rectilinear flow of heat. Ingen Hausz’s Experiment
Radiation
Blackbody radiation and its spectral distribution, Concept of the energy density, Derivation of the Planck's law, Deduction of the Stefan-Boltzmann law, the Rayleigh-Jean’s law and the Wien’s displacement law from Planck’s law.
Thermodynamics
Unit 1: Definitions: A thermodynamic system and its surroundings, Open, closed, adiabatic and isolated systems, Thermodynamic variables: extensive and intensive, Steady state of a thermodynamic system, Thermodynamic equilibrium, Thermodynamic path, Thermodynamic processes: Cyclic, Quasi-static, Reversible and irreversible processes, Isothermal, Isobaric and Isochoric processes, Minimum number of state variables for a single and a multi component system, Equation of state, Functions of state and functions of path (Examples), Exact and inexact Differentials, Heat and Work, Standard temperature and pressure, Internal energy of a system (U).
Unit 2: The zeroth law of thermodynamics and the concept of temperature, The first law of thermodynamics (differential form dU = dQ − dW), dU - an exact differential, dQ and dW - inexact differentials, Heat capacity: CV and Cp. Molar heat capacity c_v and c_p and, Ideal gas: Isothermal expansion, adiabatic transformation.
Unit 3: A heat engine, A heat reservoir, The second law of thermodynamics: Clausius’ statement of the second law of thermodynamics, Kelvin’s statement of the second law of thermodynamics, the efficiency (η) of an engine and the coefficient of refrigeration (κ), A Carnot engine, Carnot’s theorem, Working substance, The Carnot cycle in a p-V diagram with an ideal gas as working substance and four stages: isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression, the work done and the heat exchange in each stage, The efficiency of a Carnot engine (η) in terms of the ratio of T1 (temperature of the hot reservoir) and T2 (temperature of the cold reservoir), Equivalence of Clausius’ and Kelvin’s statements, A refrigerator and a heat engine, Clausius’ theorem and Clausius inequality.
Unit 4: Definition of entropy, Change in entropy (dS) for a thermally isolated system for a reversible change and an irreversible change, Application to the Universe, The first law revisited: dU = TdS – pdV, dU = dQ + dW (always true), dQ = TdS (only true for reversible changes), dW = -pdV (only true for reversible changes), dU = TdS − p dV (always true), For irreversible changes: dQ ≤ T dS, dW ≥ − pdV, Second law of thermodynamics in terms of entropy, The change of entropy in the gas, surroundings and the universe during Joule expansion of an ideal gas.
Unit 5: Thermodynamic potentials: Internal Energy (U), Enthalpy (H), Helmholtz Free Energy (F), Gibb’s Free Energy (G), dU = TdS - pdV, dH = TdS + V dp, dF = -SdT - pdV, dG = -SdT + V dp, Maxwell’s relations: Derivation and applications of expressions:
(1) (∂Cp/∂p)T and (∂CV /∂V )T in terms of p, V, T,
(2) Cp− CV = VTβ2 p/κT ,
(3) S = CV ln T + R ln V + constant, = Cp ln T - R ln p + constant for 1 mole of an ideal gas,
Isothermal (κT) and adiabatic (κS) compressibilities, Ratio of κT and κS equal to Cp / CV.
Unit 6: Free adiabatic expansion of a perfect gas, Joule-Thomson porous plug experiment. Joule- Thomson effect for real and Van der Waals’ gases. Temperature of inversion. Joule-Thomson Cooling.
Unit 7: Third law of thermodynamics: Nernst’s statement, Planck’s statement, Simon’s statement, Consequences: (a) Heat capacities tend to zero as T → 0, (b) Thermal expansion stops, (c) No gases remain ideal as T → 0, (d) Impossible to attain T = 0 in a finite number of steps.
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