Tiêu đề 13. Thermodynamics.pdf ✅

Thermodynamics 277 13 Thermodynamics QUICK LOOK Thermodynamic System A collection of an extremely large number of atoms or molecules confined within certain boundaries such that it has a certain value of pressure, volume and temperature is called a thermodynamic system. Anything outside the thermodynamic system to which energy or matter is exchanged is called its surroundings. Thermodynamic system may be of three types: Open system: It exchange both energy and matter with the surrounding. Closed system: It exchange only energy (not matter) with the surroundings. Isolated system: It exchange neither energy nor matter with the surrounding. Thermodynamic Variables and Equation of State A thermodynamic system can be described by specifying its pressure, volume, temperature, internal energy and the number of moles. These parameters are called thermodynamic variables. The relation between the thermodynamic variables (P, V, T) of the system is called equation of state. For μ moles of an ideal gas, equation of state is PV = μRT and for 1 mole of an it ideal gas is PV = RT. For μ moles of a real gas, equation of state is 2 2 ( ) a P V b RT V μ μ μ     + − =   and for 1 mole of a real gas it is 2 ( ) a P V b RT V     + − =   . Thermodynamic Equilibrium: When the thermodynamic variables attain a steady value i.e. they are independent of time, the system is said to be in the state of thermodynamic equilibrium. For a system to be in thermodynamic equilibrium, the following conditions must be fulfilled. Mechanical equilibrium: There is no unbalanced force between the system and its surroundings. Thermal equilibrium: There is a uniform temperature in all parts of the system and is same as that of surrounding. Chemical equilibrium: There is a uniform chemical composition throughout the system and the surrounding. Thermodynamic Process: The process of change of state of a 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 Isothermal process, Adiabatic process, Isobaric process, Isochoric, Cyclic and non-cyclic process, Reversible and irreversible process Zeroth Law of Thermodynamics: When two bodies A and B are in thermal equilibrium with a third body C then A as well as B are thermal, equilibrium mutually, i.e., if , T T B C = then . T T A B = Figure: 13.1 First Law of Thermodynamics: First law of thermodynamics is equivalent to law of conservation of energy. When heat energy is supplied to a gas, two things may occur: the internal energy of the gas may change and the gas may do external work by expanding. According to this law if heat ∆Q is added to a system then it will show up either as a change in internal energy dU of the system and/or as work ∆W per formed by the system i.e., ∆ = + ∆ Q dU W (all are in same unit) Figure: 13.2 Table 13.1: First Law of Thermodynamics Applied to Different Processes S.No Process ∆Q – dU + dW 1 Cyclic ∆W 0 Area of the closed curve 2. Isochoric ∆U μCv ∆T μC T v∆ 0 3. Isothermal ∆W 0 log f e i V RT V μ       4. Adiabatic 0 –∆W ( ) (1 ) μR T T f i γ − − 5. Isobaric μCp ∆T μCv ∆T ( ) ( ) f i f i p V V R T T − = − μ Q Qin – Qout W Wout – = ∆ Q Win= ∆ W System dU = ∆Q – ∆W A 10 °C 50 °F B 10 °C 50 °F C 10 °C 50 °F A in equilibrium with B B in equilibrium with C
278 Quick Revision NCERT-PHYSICS Equivalence of Heat and Work:W JQ = where W ms T = Σ ∆ If W is in joule and Q in kilo cal, then 3 J J = × 4.2 10 / kilo cal Work done by a thermodynamic system 2 1 V V W P dV = = ∫ Area enclosed by P V− curve and V-axis Figure: 13.3 In a cyclic process work done is equal to are enclosed by cyclic process on P V− diagram. Heat and work depend on path followed between initial and final configurations. Figure: 13.4 Isothermal Process: In this process, T = constant and for given mass of gas PV = constant. In isothermal process work done: 2 10 1 2.3 log V W nRT V   =     Figure: 13.5 In P-V diagram or indicator diagram, the area under P-V curve represents work done. W = area under P-V diagram, It is positive if volume increases (for expansion), It is negative if volume decreases (for compression) Figure: 13.6 P-V Diagram Adiabatic Process: In this process total heat of system Q = constant and for given mass of gas PVγ = constant, 1 PVγ − = constant and 1 T P γ γ − = constant 5 / 3 for monationic gas 7 / 5 for diatomic gas 4 / 3 for polyatomic gas P V C y C  =  = =    = When different moles of different gases are mixed, mean of γ is not taken, but mean of CP and Cv may be taken 2 1 2 mean 1 2 ( ) v v v n C C C n n + μ = + mean mean ( ) ( ) C C R p v = + and mean mean mean ( ) ( ) p v C C γ = mean γ is directly found by 1 2 1 2 1 2 1 1 1 n n n n γ γ γ + = + − − − Mayer’s formula for specific heat C C R P v − = (all in same unit) In adiabatic process work done ( ) 2 1 1 nR W T T γ = − − In isobaric process, W P V P V V = ∆ = − ( 2 1 ) In isochoric process, W = 0 Figure: 13.7 Second Law of Thermodynamics Kelvin’s statement: It is impossible for an engine operating in a cyclic process to extract heat form a reservoir and convert it completely into work, i.e., whole of heat can never be converted into work though whole of work can be Volume Adiabati Isotherma Isobaric Isochoric Pressure P A V Positive work Expansion B P A V Negative work Compression B P V Positive work P1 P2 B C D A V1 V2 Clockwise cyclic process P V Negative work P1 P2 B D C A V1 V2 Anticlockwise cyclic process p v Work done Isotherms Adiabatic process P V Path A 1 2 Path B Thermometer Insulated container Paddle Known mass of water Joule’s Heat apparatus of 1845 Weight falls through height, n W