PHYS 310: Thermodynamics and Statistical Mechanics Assignment 4: Due Thursday, November 13 at 4pm Submit into box marked PHYS310 opposite CCIS L2-041 In all questions below, give your answer in SI metric units unless otherwise specified. 1. This question provides some intuition for the effect of pressure upon the change of density of sea water. (a) Given that the thermal expansion coefficient for water is αT ≡ (−1/ρ)(∂ρ/∂T ) ≃ 2.1 × 10−4 K−1 , find the change of density for water that cools by 1◦ C. Now use the conservation of potential density for sea water to find how deep water at the surface must descend adiabatically so that its density changes by the same amount. (b) Given the relative density change of sea water with salinity S is αS = (1/ρ)(∂ρ/∂S) = 7.4 × 10−4 ppt−1 , find the change of density of sea water that has fixed temperature but becomes more saline by 1 ppt. As in (a) find the depth to which water must descend so that its density changes by this amount. 2. The density of ice is 917 kg/m3 . Its latent heat of fusion is Lf = 3.33 × 105 J/(kg). a) Use the Clausius-Clapeyron relation to explain why in a P-T diagram for H2 O the slope of the phase boundary between ice and water is negative. b) How much pressure would you have to put on a 30 cm3 ice cube to make it melt at −1◦ C. (Give your answer in bars.) c) Approximately how deep under a glacier would you have to be before the weight of ice above gives the pressure you found in part (b)? (Give your answer in km, accurate to two digits.) (This mechanism provides lubrication which accelerates the advance of a thick glacier flowing down valleys.) 3. The approximate formula for the saturation vapour pressure is 1 Lv 1 , − es (T ) = e0 exp Rv T 0 T in which T0 = 273.16 K, e0 = 6.11 mbar, Lv = 2.50 × 106 J/(kg) and Rv = 461 J/(kg K). Air at temperature T = 5◦ C has a relative humidity of 85%. Find the partial vapour pressure (in mbar) and the dew point Td (in ◦ C). 4. A parcel of moist air at the ground (where p = p0 = 1 bar) is at its dew point temperature of 5◦ C. The parcel is carried upward cooling until it loses all of its contained water. Thereafter it descends adiabatically back to the ground. What is the temperature of this dry parcel of air (in ◦ C)? 5. Consider the production of ammonia from nitrogen and hydrogen through the reaction N2 + 3H2 → 2NH3 at 298 K and 1 bar pressure. The enthalpy, H, and entropy, S, of one mole of the constituents are Substance H [kJ] N2 0 H2 0 NH3 -46.11 S [J/K] 191.61 130.68 192.45 a) Compute the Gibbs free energy required to make one mole of ammonia through this reaction. b) Compute the change in internal energy of the system during the creation of one mole of ammonia. In a) and b) give your answer in kJ, accurate to 3 digits.