1. Results of Midterm 2 0 102030405060708090 points # of students GradePoints A85-100 B+B+ 75-84 B60-74 C+C+ 50-59 C30-49 D,F<30 100

2. Problem 1 vdW gas (25) For N 2, the vdW coefficients are N 2 a = 0.138 kJ·liter/mol 2 and Nb = 0.0385 liter/mol. Evaluate the work of isothermal and reversible compression of N 2 (assuming it is a vdW gas) for n=3 mol, T=310 K, V 1 =3.4 liter, V 2 =0.17 liter. Compare this value to that calculated for an ideal gas. Comment on why it is easier (or harder, depending on your result) to compress a vdW gas relative to an ideal gas under these conditions. Depending on the interplay between the first and second terms, it’s either harder or easier to compress the vdW gas in comparison with an ideal gas. If both V 1 and V 2 >> Nb, the interactions between molecules are attractive, and  W vdW <  W ideal However, as in this problem, if the final volume is comparable to Nb, the repulsive forces at short distances become more significant than the attractive forces at large distances (an increase of the second term overpowers the negative first term). Under these conditions, it is harder to compress the vdW gas rather than an ideal gas. The work done on compression of the vdW gas: r U pot

3. Problem 2 vdW+heat engine (30) Consider a Carnot cycle where the working substance is a van der Waals gas (1-2 and 3-4 are isotherms, 2-3 and 4-1 – adiabats). The temperatures of the hot and cold reservoirs are T H and T C, respectively. Calculate the efficiency of this heat engine and compare it with that for the Carnot cycle with an ideal gas. 1 – 2 isothermal expansion (at T H ) TCTC P V THTH 1 2 3 4 V1V1 V2V2 V3V3 V4V4 Similarly,

4. Problem 3 vdW+heat engine ( cont.) 2 – 3 and 4 – 1 – adiabatic+quasistatic=isentropic processes We need to consider these processes to relate V 1, V 2, V 3, V 4 adiabatic process for vdW gas TCTC P V THTH 1 2 3 4 V1V1 V2V2 V3V3 V4V4 - the same as for the ideal-gas Carnot cycle

5. Problem 3 (phase transformations) (25) 1 kg of water at 20 0 C is converted into ice at -10 0 C (all this happens at P = 1 bar). The latent heat of ice melting L melt = 334 kJ/kg, the heat capacity of water at constant pressure is 4.2 kJ/(kg·K) and that of ice 2.1 kJ/(kg·K), the heat of fusion of ice at 0 0 C is 336 kJ/kg. (a) What is the total change in entropy of the water-ice system? (b) If the density of water at 0 0 C is taken as 10% greater than that of ice, what is the slope of the melting curve of ice at this temperature? Give both sign and size. 3 From 0 0 C to -10 0 C: 2. Melting of ice 1. From 20 0 C to 0 0 C: (a) (b)

6. Problem 4 (chemical reaction + Gibbs) (20) Consider the reaction of oxidation of methane: For this reaction  H = -164 kJ/mol,  S = -162 J/mol  K. (b) The maximum “other” work: For reversible processes: (a)Find the temperature range where this reaction proceeds spontaneously. (b)What is the maximum “other” work that the system can perform at T = 300 K? (c)What is the change in the entropy of environment,  S env, and the total entropy change for the “Universe” (the system + environment) (assume that this process is reversible)? (a) For this reaction to proceed spontaneously,  G must be negative: (c)