Volume Changes Physics 313 Professor Lee Carkner Lecture 19

Exercise #18 Steam Tables  Boiling water at low pressure  From chart P = 75 kPa, T = C and T = 100 kPa, T = C    Cover with heavy lid  P lid = F/A = mg/  r 2 = [(4)(9.8)/(  )(0.1) 2 ] = 1.25 kPa   Now have a factor of between table values  

Solids  Solids will hold a volume even in conditions of low external pressure   Need to be able to accurately measure small changes to find expansivity and compressibility

Volume Expansivity  How does the size of a a solid object change with temperature?  Need to find volume expansivity   For isotropic materials:   where  is the linear expansivity:  = (1/L)(dL/dT)  Note that some materials are non-isotropic 

Optical Interferometer  To find  and thus  need to measure small change in linear dimension   Separate two semi-transparent plates with a ring of the material in question   Each interference fringe that moves past a reference point indicates ½ wavelength of changed size

Determining   If N fringes pass the field of view, than the change in size (from L 0 to L) is:  The relative change is: (L - L 0 )/L 0 = ½N / L 0  Or:  = d/dT (½N / L 0 ) 

Variation of  with T   Rises sharply with T and then flattens out    Variations are only weakly dependant on pressure (for solids)

Compressibility  How does volume change with pressure?   = -(1/V)(dV/dP)   Adiabatic compressibility is also isentropic

Determining  s  The adiabatic compressibility can be found for a fluid by measuring the speed of sound (pressure) waves   For a crystal solid have to measure both shear and pressure waves 

 and  S  How are  and  s related?  by the heat capacities:  c P –c V = Tv  2 /    We can combine equations to get:  -  S = Tv  2 /c P

Variations of  with T  Unlike  approaches a constant at 0 K   Values tend to rise linearly at higher T for solids  Liquids generally have an exponential rise of  with T:   Liquids also have a linear increase of  with P 

Heat Capacity at Constant Volume  Can find c V with Mayer relation  How does c V (molar heat capacity) vary with temperature?    At the Debye temperature, c V approaches 3R   For all substances, c V versus T curves have a similar shape, but each substance may have different Debye temperatures

Entropy and Heat Capacities  How are the entropy and heat capacities related? dS = dQ/T (dQ/dT) = T (dS/dT)  Can calculate entropy change from C:   Where C is C P or C V depending on if the process is isobaric or isochoric

The TS Diagram   Generally have solid at low T and low S and gas at high T and high S 