CLASS 11th
Thermodynamics
Thermodynamics
01. Thermal Equilibrium and Temperature Two systems are said to be in thermal equilibrium with each other, if they are at the same temperature.
02. Zeroth Law of Thermodynamics It states that if two systems A and Bare in thermal equilibrium with a third system C, then A and B must be in thermal equilibrium with each other.
03. A Few Definitions (i)
Thermodynamic System An assembly of extremely large number of particles having a certain value of pressure, volume and temperature is called a thermodynamic system. For example, a large collection of gas molecules is a thermodynamic system. (ii) Thermodynamic Variables The variables which determine the thermodynamic behaviour of a system are called thermodynamic variables. The quantities like pressure (P), volume (V) and temperature (T) are thermodynamic variables. There are some other thermodynamic variables, such as internal energy (U), entropy (S), etc. All other thermodynamic variables can be expressed in terms of P, V and T. (iii) Equation of State A relation between pressure, volume and temperature for a system is called its equation of state. The state of a system is completely known in terms of its pressure, volume and temperature. For example, for 1 mole of an ideal gas, the equation of state is PV = RT In a simple system, such as a gas contained in a cylinder, any two variables out of the three variables P, V and T determine the state of the system. The third v ariable can be known by using the equation of state. (iv) Thermodynamic process A thermodynamic process is said to be taking place, if the thermodynamic variables of the system change with time. IN practice, the following types of thermodynamic processes can take place : (a) Isothermal Process : A thermodynamic process that takes place at constant temperature is called isothermal process. (b) Isobaric Process : A thermodynamic process that takes place at constant pressure is called isobaric process. (c) Isochoric Process : A thermodynamic process that takes place at constant volume is called isochoric process. (d) Adiabatic Process : A thermodynamic process in which no heat enters or leaves the system is called adiabatic process.
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Thermodynamics
(e) Cyclic Process : A thermodynamic process in which the system returns to its original state is called a cyclic process.
04. Work done during Expansion Total work done is given by
...(i)
By Indicator Diagram Suppose that the initial state (P1, V1) and the final state (P2, V2) of the system are represented by the points A and B on the P-V diagram as shown in fig.
Let a be any point on the indicator diagram and P and V be the values of pressure and volume corresponding to it. Suppose that volume increases to V + dV corresponding to point b on the indicator diagram, such that the pressure remains constant. Then, a a＇= b b＇ = P, the constant pressure on the system and a＇b＇= dV, increase in volume Now, small work done during the change of the system form the state a to state b dW = P dV = a a＇× a＇b＇ = area of the shaded strip abb＇a＇ The total work done by the gas during expansion from the intial state A (P1, V1) to the final state B (P2, V2) can be obtained by adding the areas of all strips such as a b b＇a＇formed between AA＇ and BB＇ under the P-V diagram. Obviously, the total work done will be W = area ABB＇A＇ ...(ii) Thus, work done by a system is numerically equal to the area under the P-V diagram.
05. First Law of Thermodynamics First law of thermodynamics is, in fact, the law of conservation of energy. According to the law of conservation of energy, the energy can neither be created nor it can be destroyed but can change itself from one form to another.
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Thermodynamics
The first law of thermodynamics extends this law, so as to include heat energy and internal energy of system. According to first law of thermodynamics, if an amount of heat dQ is added to a system, a part of it may increase its internal energy by an amount dU, while the remaining part may be used up as the external work dW done by the system. Thus, if dQ, dU and dW all are in same units, then dQ = dU + dW ...(i) Consider as gas enclosed in a cylinder provided with a frictionless and weightless piston. suppose that corresponding to the initial state A, pressure and volume of the gas are P and V respectively. Further, suppose that the piston moves through an infinitesimally small distance dx at constant pressure P [fig.], so that its volume in the final state B becomes V + dV. Then, the small work done, dW = force on piston × dx
If a is are of cross-section of the piston, then force on the piston will be equal to P a. Therefore, dW = P a × dx = P × (a dx) Now, a × dx = dV, the small increase in volume. Therefore, dW = P dV Hence, the equation (i) may be rewritten as dQ = dU + P dV ...(ii)
06. Two Specific Heats of a Gas (i)
Specific Heat of a Gas at Constant Volume It is defined as the amount of heat required to raise the temperature of 1 g of a gas through 1oC at constant volume. It is denoted by cv. Molar Specific Heat at Constant Volume It is defined as the amount of heat required to raise the temperature of 1 mole of a gas through 1oC at constant volume. It is denoted by Cv. If M is the molecular weight of the gas, then Cv = M cv
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Thermodynamics
(ii)
Specific Heat of a Gas at Constant Pressure It is defined as the amount of heat required to raise the temperature of 1 g of a gas through 1oC at constant pressure. It si denoted by cp. Molar Specific Heat of a Gas at Constant Pressure It is defined as the amount of heat required to raise the temperature of 1 mole of a gas through 1oC at constant pressure. It is denoted by Cp. Obviously, Cp = M cp
07. Work Done during Isothermal Process
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P Wiso = 2.303 R T log10 P
...(i)
V Wiso = 2.303 r T log10 V
...(ii)
Thermodynamics
AIIMS Exercise (1) 1. A certain amount of heat energy is supplied to a diatomic ideal gas which expands at constant pressure. What fraction of heat energy is converted into work? (c) (d)
(a) 1 (b)
2. When 2 moles of hydrogen is heated from 0°C to 20°C at constant volume, its internal energy changes by 400 J. The the molar specific heat of hydrogen at constant volume in JK−1mol−1 is about : (a) 10 (b) 20
(c) 40 (d) 10.5
3. P–V plots for two gases during adiabatic processes are shown in figure. Plots 1 and 2 should correspond respectively :
(a) He and O2 (b) O2 and He
(c) He and Ar (d) O2 and N2
4. A thermodynamic process is shown in figure such that PB = 6 × 104Pa, VA = 4 × 10−3 m3 and VA = 4 × 10−3 m3. In the process AB, 300 J of heat is added to the system and in process BC, 100 J of heat is added to the system, then the change in internal energy of the system in the process AC is :
(a) 200 J (b) 280 J
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(c) 240 J (d) 320 J
Thermodynamics 5. The efficiency of a Carnot’s engine is 50% and temperature of sink is 500 K. If the temperature of source is kept constant and its efficiency raised to 60%, then the required temperature of sink will be : (a) 100 K (b) 500 K
(c) 600 K (d) 400 K
6. The graph between P and T of an ideal gas is shown in figure. Find the work done by the gas in going from state A to state B.
(a) (b)
(c) (d) zero
7. The Fig. shows P–T graph for a gas heated at constant pressure. What happens to the mass of the gas from state (1) to state (2)?
(a) (b) (c) (d)
Decrease Increase Remains constant Cannot be said
8. One mole of a gas expands with temperature according to the relation V = kT4/5. Calculate work done when the temperature changes by 80 K. (a) 40 R (b) 50 R
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(c) 54 R (d) 64 R
Thermodynamics 9. An ideal gas obeys the law VP2 = constant. The gas is initially at temperature T and volume V. Find the temperature when volume changes to 2V. (a) T (b)
(c) 2T (d)
10. An ideal monoatomic gas at 27°C is compressed adiabatically to times of its present volume. The increase in temperature of the gas is : (a) 402°C (b) 375°C
(c) 475°C (d) 175°C
In each of the following questions, a statement of Assertion (A) is followed by a corresponding statement of Reason (R). Of the following statements, choose the correct one. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not correct explanation of A. (c) A is true but R is false. (d) A is false but R is true. (e) Both A and R are false. 11. (A) : A woolen clothes keep the body warm in winter. (R) : Air is a bad conductor of heat. 12. (A) : Bodies radiate heat at all temperatures. (R) : Rate of radiation of heat is proportional to the fourth power of absolute temperature.
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