1. Heat & The First Law of Thermodynamics
Chapter 17
Heat & The First Law of Thermodynamics

2. Breaking of equilibrium changing of state
Thermal processes
Breaking of equilibrium
changing of state
If the process is extremely slow, or quasi-statical
system always at equilibrium state in the process
Shown in PV diagram P V  2 1
Point: equilibrium state
Curve: quasi-statical process 2

3. Heat as energy transfer
Heat is not a fluid substance
and not even a form of energy
calorie: amount of heat to raise 1g water by 1℃
Joule’s theory & mechanical equivalent of heat
Heat is energy that transferred from one body to another because of a difference in temperature

4. The sum total of all the energy of all molecules
Internal energy
The sum total of all the energy of all molecules
—— thermal energy / internal energy
Temperature, heat and internal energy
Internal energy of monatomic (1-atom) ideal gases:
n-atoms molecule, real gases, liquids & solids 4

5. The first law of thermodynamics
The change in internal energy of a closed system, will be equal to the heat added to the system minus the work done by the system.
This is the first law of thermodynamics
where Q is the net heat added to the system
and W is the net work done by the system
U is a state variable, but Q and W are not 5

6. Consider the gas in a cylinder with a piston
Calculating the work
Consider the gas in a cylinder with a piston
Work done by the gas to move the piston dx : dx
. . . P S dV
For a finite change in volume from VA to VB : B A P V 6

7. Heat in process
Example1: In process abc, 800J heat flow into the system, and 500J work done by system. In process cda, 300J work done to system, What’s the heat?
Solution: First law P V a b c d
ΔU is different! 7

8. Isothermal process: ( constant T )
3 simple processes
Isothermal process: ( constant T ) B A P V VA VB
Isobaric process: ( constant P ) P V VA VB A B C
Isochoric process: ( constant V ) 8

9. Adiabatic process: ( Q = 0 )
No heat is allowed to flow into or out of system
Well insulated or process happens too quickly
Adiabatic curve is steeper than an isothermal curve B A P V
isothermal C
adiabatic
Temperature decreases as well 9

10. Solution: In process ab:
Cyclic process
Example2: An monatomic (1-atom) gas system goes through processes ab, bc, ca. Determine Q, W and ΔU in each process.
Solution: In process ab: c
P (105Pa)
4 V ( l ) 2 o a b 1 3 10

11. In process bc: In process ca: P (105Pa) c b a o Q, W and ΔU
4 V ( l ) 2 o a b 1 3
In process ca:
Q, W and ΔU
in process abca? 11

12. Heat transfer in → temperature rises
Specific heat
Heat transfer in → temperature rises
c is called the specific heat of material
For water at 15℃ and 1atm:
one of the highest specific heats of all substance
c as constant (P407, T17-1)
except for gases 12

13. c for gases depend on how the process goes on
Molar specific heat
c for gases depend on how the process goes on
Heat required to raise 1mol gas by 1℃ (conditions)
Isochoric (constant V) CV:
Isobaric (constant P) CP:
For CV of monatomic (1-atom) ideal gas, W = 0 13

14. What is CV of diatomic or triatomic gas?
Degrees of freedom
What is CV of diatomic or triatomic gas?
Degrees of freedom: number of independent ways molecules can possess energy.
monatomic:
i = 3
diatomic:
i = 5
triatomic:
i = 6 14

15. Equipartition of energy
Principle of Equipartition of energy:
Energy is shared equally among the active degrees of freedom, each degree of freedom of a molecule has on the average energy equal to kT/2.
Average energy of a molecule:
Internal energy: 15

16. CV of diatomic gases by experiments:
Active DoF & CV
CV of diatomic gases by experiments:
Active degrees of freedom at different T
Translational motion;
Rotation;
Vibration
i = 3, 5, 6 for 1, 2, n-atoms
Isochoric molar specific heat: 16

17. Solution: (a) Active degrees of freedom: i = 5
Energy in gas system
Example3: Determine the internal energy of (a) 2l O2 gas system at 1atm; (b) same system at same T but O2 is dissociated to 2O.
Solution: (a) Active degrees of freedom: i = 5
(b) O2 dissociate to 2O: i = 3 17

18. Isobaric molar specific heat CP
In an isobaric process (constant P):
Isobaric molar specific heat:
Adiabatic coefficient 18

19. Equation for adiabatic curve?
Adiabatic equation B A P V
isothermal C
adiabatic
Equation for adiabatic curve?
Equation of quasi-static adiabatic process 19

20. 1) Isothermal / adiabatic C ?
Some questions P V
1) Isothermal / adiabatic C ?
2) Why
3) Monatomic / diatomic / triatomic gas
4) Process AC is adiabatic
adiabatic B A P V C D
then does heat flow in or out in process AB and AD? 20

21. Isobaric & adiabatic
Example4: N2 system compresses isobarically in process AB, and then expands adiabatically to C. (a) Q in process AB; (b) PC ; (c) W in process BC.
Solution: (a)
(b) P V C A B 3V
isothermal ?
(c) 21

22. Solution: No heat flows in or out → Q = 0
Free expansion
Example5: 2 well-insulated container. A is filled with gas and B is empty. Open the valve, there is an adiabatic free expansion. What is the final P, T ?
Solution: No heat flows in or out → Q = 0
No work is done → W = 0
U doesn’t change in free expansion!
PA , TA , V V
Not quasi-static, no PV diagram 22

23. *Heat transfer
Conduction:
Convection:
Radiation: 23