Aheat exchanger is to cool ethylene glycol (cp = 2.56kj/kg·◦c) flowing at a rate of 3.2kg/s from 80◦c to 40◦c by water (cp = 4.18kj/kg·◦c) that enters at 20◦c and leaves at 70◦c. determine (a) the rate of heat transfer (b) mass flow rate of water.

a)

b)

Explanation:

A)

Consider the energy balance just for the ethylene glycol; we can write an energy balance for this compound because it does not mix with any other.

The heat is negative for this balance because the energy in heat form is going out of the ethylene glycol.

B)

Consider the same energy balance, but for water:

The heat that the ethylene glycol losts is the same that the water receives, so, for this equation Q is the same quantity that we found above, but with a positive sign because it is entering to the water.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.