Question

(1) A pig lying on a 2.0 cm thick wood floor has its belly in contact with the floor. Let the contact surface area of pig's belly and floor floor be 3000 cmn'. The floor is cooler than the pig's body temperature (30°C), and at a temperature of 0.0 °C. The thermal conductivity of wood is 0.126 W/m °K. What is the conductive heat transfer under steady-state conditions? (2) The Born energy EB (SI unit kcal/mol) is a measure of the impermeability of mem- brane to ions. Let us consider a fully charged group of arginine, aspartic acid and glutamic acid ion of radius r = 2.5 and valence Z = 1. The dielectric constants of the lipid bilayer and water are em = 78 and ew = 2, respectively. The membrane is considered a barrier, and represents the energy difference between the ion's electric field in the membrane and in water. Find the Born energy for this ion and the lipid bilayer. Ep = 695 ( 4 1) The Born energy can be thought of as the "activation energy" for a single ion's translocation though the membrane. In terms of the free energy, the Boltzmann factor can be defined as e-AG/RT, where the Universal Gas constant Ris 8.314 J/mol. Determine the probability that the ion will make it through the membrane. Is it likely to penetrate the membrane? We assume a core body temperature of 310 °K. Finally, normal core body temperatures can range from 36.5-37.5 °C. If the body is outside this range then it could be fatal. Plot the probability as a function of temperature from 35 to 41 °K. Is it better for an ion to penetrate the membrane when a core body temperature is cooler or hotter? (3) First, you heat 2.5 kg of water initially at 25°C to 100 °C, then you boil off the water into steam and raise its temperature to 150 °C. Compute the total energy needed in this process. Find the entropy at each stage and determine the total entropy for this process. The specific heats and latent heat of evaporation for dihydrogen oxide (or H2O) are water = 4.2 x 10° J/kg ⓇC, Ceteam = 2.0 x 10'J/kg °C, and L. = 2,260 kJ/kg (4) The chemical reaction H + 10 + H2O is carried out at a constant pressure of 1 atm and a constant temperature of 25°C. This reaction produces water, which is important to all biological processes. What quantity of heat Q will cross the system boundary and in which direction)? For this reaction, the change in internal energy is AU = -240.59 kJ/mol. In our case, the amount of work done by the surroundings for the reaction to occur is 1.24 kJ.

Answer 1

Question (1) given L=2 cm = 2x152 m A = 3000 km2 = 3000X154 cm2 To= 30°C Ti = O'C k=0.126 w/mk Heat transfy undey steady state = K A (IT) B = 0.126 * 3000X10 4 x ( 30-0) 2x102 Q = 567 Ils