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 Midterm Exams and Solutions
1. List the properties of what we call a simple system.  4 points

2. What is Postulate 2 of  thermodynamics (Callen)?   6 points

3. 10 dm3 helium gas (T = 298 K, P = 1 bar) is compressed adiabatically to 1 dm3 (step 1), and then expanded isothermally to 10 dm3 and cooled down in a constant volume process to P = 1 bar (step 2). Calculate the internal energy change DU, the heat Q, and the work W during the two steps. (Helium can be considered as an ideal gas at these circumstances, and adiabatic compression can be described by P · V5/3 = constant. ) 6 points

4. Check if the entropy function

S = (R/q)1/2(nU)1/2exp(-(UV)/(nRqv0))
conforms with the postulates of thermodynamics.  4 points
  1. Derive the equilibrium condition from the 2nd postulate of thermodynamics in a system at constant pressure and temperature, in contact with a thermostat and a manostat. 5 points

2. Show that (d(G/T) / dT)T = - H / T 2 (which is called the Gibbs-Helmholtz equation).  5 points
     (d is for partial derivation!!)

3. Use the Maxwell relations and Euler's chain relation to express (dp / dS)V and (dV / dS)P in terms of the heat capacities, the expansion coefficient, and the isothermal compressibility.
     (d is for partial derivation!!)  5 points

4. Use the Maxwell relations to show that the volume dependence of the entropy of a perfect gas is such that S is proportional to  R ln V.  5 points
 

 Midterm Exam 3  (November 4)
1. Inside a liquid there is a cavity filled with the vapour of that liquid. Derive an expression for the pressure inside the cavity.

2. The vapour pressure of ice is 610 Pa at 0 oC and 260 Pa at -10 oC. Calculate the enthalpy of sublimation of ice.

3. Calculate the relative humidity in a cloud, consisting of droplets of 2 10-7 m diameter. The temperature is T = 25 oC and the pressure pwater = 7.2 10-2 N/m. (Relative humidity is the ratio of the actual water vapour concentration and the equilibrium concentration of water vapour over a flat water surface.)

4. By how much does the chemical potential of water supercooled to - 5.0 oC exceed that of ice at that same temperature? (Hfus = 6.01 kJ/mole; Hvap = 40.6 kJ/mole) Assume that the chemical potential of both water and ice are linear functions of temperature within the region of calculation.
 

 Last Midterm Exam  (December 17)
1. 50 g copper, of temperature 1500 K, is kept in an adiabatic container. Having added some water, of temperature 300K, to the container both solid and liquid copper can be found in it. Calculate the maximum and minimum amount of water added.
Data:  Cp(liquid water) = 75.291 J/(K mol), Cp(water vapour) = 33.58 J/(K mol), Cp(liquid copper) = 31.38 J/(K mol), Cp(solid copper) = 24.44 J/(K mol), MCu = 63.54, melting point of copper = 1357 K, deltaH(fusion, copper) = 13.050 kJ/mol, deltaH(vaporization, water) = 40.656 kJ/mol.

2. 100 g methanol and 100 g ethanol are mixed. Calculate the mole fraction of ethanol in the liquid  and in the vapour phases and the vapour pressure of the mixture. Vapour pressures of pure ethanol and methanol are 6.93 kPa and 11.83 kPa, respectively.

3. Calculate the inlet pressure required to maintain a flow rate of 8.70 cm3/s of nitrogen at 300 K flowing through a pipe of length 10.5 m and diameter 15 mm. The pressure of the gas as it leaves the tube is 1.00 bar. The volume of the gas is measured at that pressure.

4. What proportions of benzene and ethylbenzene should be mixed by mole fraction in order to achieve the greatest entropy of mixing?