xii science physics chapter no.5 thermodynamics

thermodynamics

1. MAHARSTRA STATE BOARD H S C XII SCIENCE PHYSICS BY-P.B AVHAD

2. Thermodynamics PART-II AVHAD P.B CHAPTER NO – 4

3. First Law of Thermodynamics: (Work and Heat are related) The first law of thermodynamics gives the mathematical relation between heat and work First Law of Thermodynamics C onsider the work done by the system (the gas) in increasing the volume of the cylinder. During expansion Fig(a) the gas molecules which strike the piston lose their momentum to it, and exert a pressure on it. As a result, the piston moves through a finite distance. The gas does a positive work on the piston . When the piston is pushed in so that the volume of the gas decreases Fig(b) the gas molecules striking it gain momentum from the piston. The gas does a negative work on the piston .

4. which shows a system enclosed in a cylinder with a movable,massless,and frictionless piston so that its volume can change. Let the cross sectional area of the cylinder be A , and the constant pressure exerted by the system on the piston be p . The total force exerted by the system on the piston will be F = pA If the piston moves through an infinitesimal ( very small ) distance dx , BUT T he work done by this force is, But

5. When the amount of heat Q is added to the system and the system does not do any work during the process its internal energy increases by the amount, Δ U = Q . The system loses energy to its surrounding and its internal energy decreases. This means that when W is positive , Δ U is negative and, vice versa. Therefore, we can write , Δ U = - W . Therefore, we consider the effect of both together and write the total change in the internal energy as, Δ U = Q -W This is the mathematical statement of the first law of thermodynamics Q = Δ U +W First law of Thermodynamics - when the amount of heat Q is added to a system, its internal energy is increased by an amount Δ U and the remaining is lost in the form of work done W on the surrounding.

6. Thermodynamic state variables-: Thermodynamics is not the study of changes in temperature of a system only. As we have seen earlier, when temperature of a system changes ( it gains or releases energy), its other properties can also change. Let us understand these properties. We will define the term property of a thermodynamic system first Property of a system or a system variable: It is any measurable or observable characteristic or property of a system when the system remains in equilibrium A property is also called a state variable of the system Intensive and Extensive variables: Intensive variables do not depend on the size of the system i.e. pressure p , temperature T , density ρ Extensive variables depend on the size of the system . i.e. The mass M , and the internal energy U

7. Thermodynamic Equilibrium: if the following three conditions of equilibrium are satisfied simultaneously. Mechanical equilibrium- When there are no unbalanced forces within the system and between the system and its surrounding , the system is said to be in mechanical equilibrium Chemical equilibrium : A system is said to be in chemical equilibrium when there are no chemical reactions going on within the system, Thermal equilibrium : When the temperature of a system is uniform throughout and does not change with time, the system is said to be in thermal equilibrium

8. Thermodynamic State Variables and Equation of State-: Every equilibrium state of a thermodynamic system is completely described by specific values of some macroscopic variables , also called state variables. S ystem which is not in equilibrium cannot be described in terms of the state variables The mathematical relation between the state variables is called the equation of state . Where, p , V and T are the pressure, the volume and the temperature of the gas, n is the number of moles of the gas and R is the gas constant For a fixed amount of the gas, i.e., for given n , there are thus, only two independent variables It could be p and V , or p and T , or V and T . For example , pressure p , volume V , temperature T , and mass m .

9. The graphical representation of equation of state of a system (of a gas) is called the p - V diagram, or the p - V curve p-V diagram for an ideal gas at some constant temperature . The pressure-volume curve for a constant temperature is called an isotherm

10. The p - V diagram: Consider Since this integral represents the work done in changing the volume of the gas T he area under the p-V curve also represents the work done in this process . for expansion of the gas the pressure of the gas decreases. The work done by the gas in this case is positive because the volume of the gas has increased .

11. For compression due to inward displacement of the piston. The pressure of the gas is increased and the work done by the gas is now negative. when the volume of the gas changes from V i to V f at a constant pressure. The curve is actually a line parallel to the volume axis. The work done during volume change at constant pressure is positive

12. When the volume is constant in any thermodynamic process, the work done is zero because there is no displacement. In the three cases we discussed, the amount of work done is not the same . The work done by a system depend not only the initial and the final state, but also on the intermediate state I.e. on the path along which the change takes place .

13. Thermodynamic Process A thermodynamic process is a procedure by which the initial state of a system changes to its final state. During such a change, there may be a transfer of heat into the system from its environment, (positive heat), for example when water boils heat is transferred to water. Heat may be released from the system to its environment (negative heat). Similarly, some work can be done by the system ( positive work ), or some work can be done on the system (negative work) I n thermodynamic equilibrium. Such processes in which changes in the state variables of a system occur infinitesimally slowly are called quasi static systems

14. Work Done During a Thermodynamic Process : The system is initially at state A on the p-V diagram . Its pressure is p i and volume is V i. We say that the state is indicated by the coordinates ( V i, p i). The final state of the system is shown by the point B with its coordinates given by ( V f , p f). When the system changes itself from A to B along the path 1, both its pressure and volume change. The pressure decreases while the volume increases. The work done by the system is positive (because the volume increases ). It is given by the area under the curve 1

15. Second way to change the state from A to state B is path 2 the volume increases to V f from the point A up to the point C at the constant pressure p i. The pressure then decrease to p f as shown . The volume remains constant during this change. The system is now in the state B with its coordinates given by ( V f , p f ). The work done in this process is represented by the shaded area under the curve 2

16. Third way to change the state from A to state B is path 3 the pressure decreases from p i to p f but the volume remains the same. Next, the volume changes to V f at constant pressure p f. The work done in this process is represented by the shaded area under the curve 3 It is easily noticed that in the three cases we discussed, the amount of work done is not the same C onclusion - The work done by a system depends not only on the initial and the final states , but also on the intermediate states, i.e. on the paths along which the change takes place .

17. Heat Added During a Thermodynamic Process : There are two different ways in which this change in volume can be made first method-- In this case, the gas is heated slowly, in a controlled manner so that it expands at a constant temperature. It reaches the final volume V f isothermally The system absorbs a finite amount of heat during this process.

18. second case- gas cylinder is now surrounded by an insulating material and it is divided into two compartments by a thin, breakable partition. The compartment X has a volume V i and the compartment Y has a volume V' I so that V i + V' i = V f . In this case, the gas has not done any work during its expansion because it has not pushed any piston or any other surface for its expansion. Such expansion is called free expansion

19. in both cases. represent two different ways of taking a system from the initial state to the final state. This means we have two different paths connecting the same initial and the final states of a system. To conclude, heat transferred to a system also depends on the path

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