1. Heat Physics 313 Professor Lee Carkner Lecture 9

2. Exercise #8 Piston  Initial pressure:  Cold position and pressure:  Hot position and pressure:  Work to lift weights:  W = mgh  h = 0.0447 m -0.0315 m =  W = (0.3 kg)(9.8 m/s 2 )(0.0132 m) =

3. Exercise #8 Piston  Work due to pressure:  Pressure is constant (102.5 kPa -99.1 kPa) =  W = ∫ PdV = P  V (isobaric process)   diameter of piston = 32.5 mm, r = 0.01625 m  A =  r 2 =  ( 0.01625) 2 =   V = hA = (0.0132)(0.0008296) = 1.095X10 -5 m 3  W = P  V = (3400)(1.095X10 -5 ) =  Compare  difference = 0.0388 – 0.03723 =  average = 0.0380 J  percent difference = [(0.0016)/0.0380)](100) =

4. Heat Capacity  The degree to which temperature is changed by heat can be expressed with:  Heat Capacity (J/K)  Specific heat (J/kg K)  Molar heat capacity (J/mol K)

5. Latent Heat   Heat can also cause a phase change with no temperature change   The latent heat (L) is the amount of heat needed (per mole or kg) to change phase

6. Vaporization and Fusion   Latent heat of fusion   Latent heat of vaporization  Heat required:

7. Using a Heat Reservoir   Called a heat reservoir   The reservoir has a constant temperature  For an isobaric process, the system needs to be in contact with a variable temperature heat reservoir

8. Heat Problems   Sum all heats to get total   Objects at different T will exchange heat until at common T   |Q 1 |= |Q 2 |= |m 1 c 1 (T f -T 1 )| = |m 2 c 2 (T f -T 2 )|  Heat reservoir has constant properties

9. Conduction  dQ / dt = -KA (dT/dx)  A is cross sectional area  K is thermal conductivity  High K =  Low K =

10. K Dependencies  K depends on the molecular properties of a substance    K depends on temperature 

12. Radiation   Total energy and wavelengths of photons depend on temperature:  Larger T --   If  = 1 substance is a blackbody   Need to find difference between emission and absorption to get net heat

13. Stefan-Boltzmann Law  Thermal radiation:  P is the power (energy emitted per second)  Stefan-Boltzmann constant:   =5.67051 X 10 -8 W/m 2 K 4  dQ/dt = A  (T env 4 - T 4 )  Note that power per unit area is the flux (F in W/m 2 )

14. Blackbody Curves

15. Blackbody Radiation  Classical physics could only describe the radiation curve with the Rayleigh-Jeans law  Problem: ultraviolet catastrophe   In 1900 Max Planck determined the true radiation law empirically   Energy is quantized

16. Convection   This will happen naturally in a fluid in a gravitational field   Cold gas will contract, increase in density and fall   What are the conditions and transport rates for convection?

17. Convective Energy Transport  Convection physically moves mass so the heat transfer depends on how much energy the mass contains and how fast it moves   F =  vcT (J/s/m 2 )  But this is only the material moving in one direction  F =  vc  T  Assuming equal densities and velocities

18. Will it Float?  Energy transport in fluids is radiative or convective  Consider a bubble of gas that is trying to rise   The density of the surrounding gas depends on the temperature gradient   i.e. if the surrounding gas cools with height faster than the bubble, the bubble will rise  Convection!

19. Convection?  Gradient of surroundings depends on radiation  The condition for convection can be written as:  Have convection when  bub is small or  rad is large   Large C V means the bubble cools off slowly and stays hotter than its surroundings   Large opacity means radiation is absorbed and doesn’t heat up upper layers very well

20. Structure of the Sun Core Radiative Zone Convective Zone Photosphere Chromosphere Corona

21. Solar Granulation

22. Which Process?  Radiation  Low density   Convection  Fluid matter, low K   Conduction  Solid matter 