1. First Law of Thermodynamics Physics 202 Professor Lee Carkner Lecture 13

2. PAL #12 Temperature  How does the Galileo thermometer work?   The water in the tube changes density with T   Water gets less dense as T rises and so the balls fall (64 to 80)  Galileo thermometer’s limitations   Not much range (64-80 F)   Only works upright and in a gravitational field

3. Heat Capacity   Put a wooden spoon in a pot of water and boil it  Which has the higher temperature?  Heat capacity (unit energy per Kelvin) is given by:  Where:  Q = heat (J)   C is a property of a specific object

4. Specific Heat  The heat capacity depends on the mass of the object and so is normally written:  Where m is the mass and c is the specific heat   Each type of substance has a c (e.g. water, iron, etc.)  Q = cm(T f - T i )  Amount of heat (Q) needed to change the temperature of m kg of a certain type of substance from T i to T f

5. Molar Specific Heat  Instead of per kilogram it is sometimes more convenient to use specific heat per mole (c mol )   We need to use a modified version of the last formula:  Good for gases

6. Heat of Transformation   Boiling water stays at 100 deg C, the added energy goes into transforming the water from liquid to gas  Q = L m  Where L is the heat of transformation

7. Vaporization and Fusion   For the phase change from solid to liquid the heat of fusion, L F is needed   The total heat necessary to change temperature and state is the sum of heats required for each

8. Phase Curve for Water

9. Calorimetry  To find total heat, add heats from all temperature and phase changes   Make sure units for m, c, L and T match  Always use  T = T f -T i   Temperature decrease results in a negative loss of heat   For a isolated system the sum of all heats is zero 

10. Work and Internal Energy   No heat can travel in or out  If weight is removed from the piston head the remaining weight will rise   Where does the energy come from? 

11. Internal Energy and Work

12. Work and Heat   The thermal reservoir can add or subtract heat from the system   What happens to the internal energy of the system as heat is applied or work is done?

13. Heat and Work

14. Work, Heat and Internal Energy  We find in every situation that the change in internal energy is equal to the change in heat minus the change in work   Energy is conserved!

15. The First Law of Thermodynamics  This conservation of energy is called the First Law of Thermodynamics  E int =  Q -  W   Sign convention: 

16. Work, Pressure and Volume  How does work change the system?   The amount of work done in moving something a small distance ds is:  However, F = pA and dV = A ds   W =  dW =  p dV (integrated from V i to V f )  Work is the area under the curve on a p-V diagram

17. p-V Diagrams

18. The p-V Curve  Pressure must be non-zero in order for work to be done    If the volume decreases, work is done on the system and the work is negative   If the process is cyclical and returns to the same point by two different paths the area between the paths is equal to the work (and also equal to the heat)

19. Adiabatic  Q=0 so  E int = -W  Consider a thermally isolated (insulated) piston with weight on top   By changing the weight, the gas is compressed or expands

20. Constant Volume   E int = Q  If any heat is applied to the system it goes directly into internal energy   The gas cannot expand

21. Cyclical Process   The final pressure, volume and internal energy are the same as the initial  E int = 0 so Q=W  