Question

Consider hot gases flowing through a pipeline shown in Fig.1. Due to heat loss to the
surroundings, the temperature of the gas decreases continuously from the inlet at
state ‘m’ to the exit at sate ‘n’. Assume a reversible isobaric path between the inlet
and exit states of the gas. Find the available energy at the two sections (infinitesimal)
shown in Fig.1. Comment on your results.

Answer 1

The total amount of heat at the beginning of the pipe: m joules.

The total amount of heat at the end of the pipe: n joules.

Loss of heat through the pipe: m-n joules.

If l be the length of the pipe, loss of heat per unit length: (m-n)/l.

If a is the area of the pipe, and dx is a small infinitesimal distance,

Available energy at a distance dx:

(m-n)*dx/la^2

There is a heat loss from the pipe when the heat is being carried from one end to the other end of the pipe because of poor insulation of the pipe. And heat loss per unit length when multiplied by the area and divided by the the length gives the energy.