ENGINEER 1C03 Chapter 20: brownian_motion.12

Let
H = {f : R → R | f(x) = ax + b; a, b ∈ R; a > 0}.
H1 = {f : R → R | f(x) = ax; a ∈ R; a > 0}.
H2 = {f : R → R | f(x) = x + b; b ∈ R}.
(a) Prove that H1 and H2 are subgroups of H.
(b) Determine whether each is a normal subgroup of H.

Match the heat transfer process in ‘A B C’ to ‘P Q R.’

1. Conduction

2. Convection 

3. Radiation 

 P. Heat transfer from one molecule to another molecule

 Q. Heat transfer does not require a medium

 R. Heat transfer through a fluid.

A conical tank (D=1.6 m, H=4 m) is initially full of a liquid (ρ=900 kg/m3). The top surface of this liquid is exposed to air; and rate of evaporation of the liquid is given to be proportional the exposed surface. The radius r for any level of the tank is given as: r = 0.8 - 0.00358t, where r is in meters, and t is time in hours. Determine the rate evaporation of the liquid, in kg/h, after 5 hours.