An aqueous solution with a boiling point 3°C above that of water is heated and partially vaporized in the tubes of a shell-and-tube exchanger. Steam on the shell side of the exchanger is at 1.70 atm gauge, and the solution enters at 28°C. Assuming an  average pressure of 1 atm in the tubes (neglect any frictional pressure drop) and 50 percent vaporization of the liquid, sketch the temperature profiles for the exchanger. What is the logarithmic mean temperature difference?