Answers

1a)

1b)88.4

1c)-81.6

1d)6.80

v Difference Form of Entropy Balance: General Equation: Sy, S, = Zi{:](ftiz Mkkdt) -+ tz th T Problem 1: The a cylinder is attached to a rectangular prism as shown in the following figure. The diameter of the cylinder is 0.5 m, and the height of the cylinder is 3 m. The length of the prism is 3 m, while the height and width are 0.8 m and 0.9 m, respectively. The thickness of the cylinder bottom is 0.015 m, and the thickness of prism wall is 0.01 m. The outer surface of the prism and cylinder is well-insulated except for the connected area. Al a specific time t, the prism is filled with liquid A with a uniform temperature of 360 K, and the cylinder is filled with liquid B with a uniform temperature of 390 K. This leads to heat transfer between the prism and the cylinder. The thermal conductivity of the connected area is 135 W/K/m. Assume this heat transfer happens slowly enough that either liquid is in approximate equilibrium at any given instant. (i.e., there is little spatial variation in temperature within each shape, and we can say S,., = U when considering either liquid separately. This is called a quasi-static process.) 0.8m 0.9m For that instant in time: a) Calculate the heat transfer rate for two subsystems (prism and cylinder) b) Calculate the entropy change for the prism subsystem c) Calculate the entropy change for the cylinder subsystem d) Calculate the entropy change of the whole system (view the combined prism and cylinder as the system) Differential Form of Entropy Balance: K neral Form: Z MkSk) + % + Sgen k1