Chapter 17 The first law of thermodynamics

1. Chapter 17 The first law of thermodynamics • Thermodynamic systems • Workdone during volume changes • Paths between thermodynamic states • Internal energy and the first law of thermodynamics • Kinds of Thermodynamic processes • Heat capacity of an ideal gas • Adiabatic processes for an ideal gas

2. Thermodynamic system • A system that can interact (exchanges energy) with its surroundings or environment is called “Thermodynamic system”. • The process they interact and change in the state of a thermodynamic system is called “Thermodynamic Process”. • The states variables involved in thermodynamic process are P, V, T, U, and W

3. Workdone during volume changes • workdone can be performed by gas system by changing volume. A = cross section area dX P P constant pressure

4. Workdone during volume changes • if V2>V1 W > 0 the system expands. “the work is done by system” • if V2<V1 W < 0 the system compresses. “the work is done on the system” P Workdone is also the area under the P-V curve. W > 0 expand W < 0 compress V

5. Path between thermodynamic states P a Isothermal process (T =constant) Pa b Va Vb V P a Pa (V =constant) Isochoric process b Pb Va =Vb V

6. Path between thermodynamic states Isobaric process (P =constant) P a b Pa Va Vb V

7. Internal energy • Internal energy is the total energy stored in the thermodynamic system. In ideal gas system, internal energy (U) is the total kinetic energy, • Internal energy can change by thermodynamic process.

8. The first law of thermodynamic • The first law arises from the relations among internal energy (U), workdone (W) and exchanged heat (Q). Heat in (Q > 0) Heat out (Q < 0) U2 U1 Thermodynamic process Work by system ( W > 0 ) Work on system ( W < 0 )

9. The first law of thermodynamic • If the process have changed by infinitesimal change, or Heat in (dQ > 0) Heat out (dQ < 0) U2 = U1 +dU U1 Thermodynamic process Work by system ( dW > 0 ) Work on system ( dW < 0 )

10. Kinds of thermodynamic process Adiabatic process No heat transfers in or out from the system ( Q =0 ). DU = U2– U1 = -W Work causes change in internal energy. W > 0 W < 0 U1 compress expand U2 < U1 U2 > U1 DU > 0 DU < 0

11. Kinds of thermodynamic process Isochoric process constant volume : No workdone ( W =0 ). DU = U2– U1 = Q Heat transfer causes change in internal energy. Heat out (Q < 0) Heat in (Q > 0) U1 U2 > U1 U2 < U1 DU < 0 DU > 0

12. Kinds of thermodynamic process Isobaric process constant pressure process. Q, W,DU are not zero. First law DU = Q - W Workdone W = P (V2–V1) W < 0 W >0 Q <0 W < 0 Q >0 Q >0 system system system DU =Q - W DU =Q +W DU =-Q +W

13. Kinds of thermodynamic process Isothermal process constant thermal process. Q, W,DU are not zero. First law DU = Q - W For ideal gas in isothermal process Q = W W >0 Q >0 W < 0 Q <0 System of ideal gas System of ideal gas Q = W -Q = -W

14. Heat capacity of an ideal gas We define two types of molar heat capacity, 1. Molar heat capacity at constant volume: CV, 2. Molar heat capacity at constant pressure: CP. P P2 Constant volume Constant pressure For ideal gas P1 T2, U2 CP > CV T1, U1 V

15. Heat capacity of an ideal gas First law For infinitesimal change, dQ = dU+dW In isochoric process (dW =0) In isobaric process dQ = dU dQ = dU +dW

16. Heat capacity Define Ratio of heat capacity For monoatomic, ideal gas For diatomic, real gas

17. Adiabatic process for an ideal gas • In adiabatic process, no heat is transferred in or out of the system (dQ =0). dU = -dW First law P a Pa The adiabatic process begin from point a ( at T+dT ) and change to lower temperature point b ( at T). The workdone by adiabatic process is the shade area. T+dT b Pb W T Va Vb

18. Adiabatic process for an ideal gas dU = -dW After integration, we get nCVdT = -PdV = - or finally n = constant

19. Adiabatic process for an ideal gas DU = -W W = nCV(T1-T2) Workdone in adiabatic process