Heat Physics 313 Professor Lee Carkner Lecture 9

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

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

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)

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

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

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

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

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

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

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

Stefan-Boltzmann Law  Thermal radiation:  P is the power (energy emitted per second)  Stefan-Boltzmann constant:   = X 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 )

Blackbody Curves

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

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?

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

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!

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

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

Solar Granulation

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