For water, the molecular weight is 18.0 gms/mole, C_p = 75.5 J/mole-K for liquid
ID: 517883 • Letter: F
Question
For water, the molecular weight is 18.0 gms/mole, C_p = 75.5 J/mole-K for liquid and C_p = 37.8 J/mole-degK for ice, and delta H_fusion = 6.01 kJ/mole a) Calculate the change in entropy when 50g. of water at 80 degree C is poured into 100g. of water at 10 degree C in an insulated vessel. b) Calculate the change in entropy when 200 g. of water at 0 degree C is added to 200 g. of water at 90 degree C in an insulated vessel. c) Calculate the change in entropy when 200 g. of ice at 0 degree C is added to 200 g of water at 90 degree C in an insulated vessel. The melting point of Cu is 1083 degree C and its heat of fusion is 11.2 kJ/mole. The heat capacities of the solid and liquid are 33.5 J/K-mole and 26.9 J/K-mole respectively. Calculate the entropy change of one mole of Cu when it crystallizes at 1073 degree C. Also find the entropy change for Cu plus surroundings, assuming the heat of fusion is relatively independent of temperature. Show that (partial differential H/partial differential P)s = V, starting with H = E + PV and an expression for dE. (also remember H = H(S,P) One mole of CO_2 gas is contained in a piston and cylinder at 300 K. At equilibrium, the volume of the gas is 1.00 liter. You may consider this to be a van der Wall's gas with a = 3.59 l^2-atm/mole and b = 0.0427 l/mole, and C_v = 0.369 l-atm/mole-deg. The cylinder is suddenly placed in a large temperature bath held at 200 K and allowed to come to equilibrium spontaneously. The final volume of the gas is 0.500 liters, and 5.00 kJ of heat is absorbed by the bath during the process. Determine the entropy change of the universe for this process. A certain solid is governed by the equation of state: v = v_0(1 - K_T(P - P_0) + alpha (T - T_0)) where alpha = 5.1 times 10^-5 K^-1, k_T = 3.2 times 10^-5 atm^-1 and beta = -(partial differential E/partial differential V)_T = 0.5 atm. Also: P_0 = 1 atm, T_0 = 293 K, and V_0 = 1 liter. Initially the solid is held in a piston and cylinder at equilibrium, such that P_1 = P_0 = 1 atm, and T_1 = T_0 = 293 K, and held in a constant temperature bath at that temperature. The system is then subjected to two constant temperature steps: I. The external pressure is kept constant while the solid is irreversibly compressed. II The external pressure is suddenly dropped to zero, and the solid is allowed to expand until V = V_0 = 1 liter, at which point the pressure is quickly restored to 1 atm. Calculate delta q, delta w, delta E, delta S_sys, delta S_universe for step I and step II.Explanation / Answer
1. Mw = 18 g/mol
Cp, w = 75.5 J/mol-K
Cp, i = 37.8 J/mol-K
Hfus = 6.01 J/mol
a) m1 = 100 g, m2 = 50 g
T1 = 10°C = 10 +273 = 283 K
T2 = 80°C = 80 +273 = 353 K
n1 = m1 / Mw = 100 g / 18 g/mol = 5.56 mol
n2 = m2 / Mw = 50 g / 18 g/mol = 2.78 mol
Change in entropy, S = (n1+n2) Cp, w ln (T2/T1) = (5.56 mol+2.78 mol) 75.5 J/mol-Kln (353 K/283 K)
= 139.17 J/K
b) m1 = 200 g, m2 = 200 g
T1 = 0°C = 0 +273 = 273 K
T2 = 90°C = 90 +273 = 363 K
n1 = m1 / Mw = 200 g / 18 g/mol = 11.11 mol
n2 = m2 / Mw = 200 g / 18 g/mol = 11.11 mol
Change in entropy, S = (n1+n2) Cp, w ln (T2/T1) = (11.11 mol+11.11 mol) 75.5 J/mol-Kln (363 K/273 K)
= 478.00 J/K
c) m1 = 200 g, m2 = 200 g
T1 = 0°C = 0 +273 = 273 K
T2 = 90°C = 90 +273 = 363 K
n1 = m1 / Mw = 200 g / 18 g/mol = 11.11 mol
n2 = m2 / Mw = 200 g / 18 g/mol = 11.11 mol
Change in entropy, S = (n1+n2) (Cp, w+Cp, i) ln (T2/T1) = (11.11 mol+11.11 mol) (75.5 J/mol-K+37.8 J/mol-K) ln (363 K/273 K) = 717.32 J/K
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