A heat reservoir is maintained at 927°C. If the ambient temperature is 27°C, the availability of heat from the reservoir is limited to

Concept:

The maximum work obtained from a certain heat input in a cyclic heat engine is often called the available energy (A.E.) of the available part of the energy supplied.

Let Q be the amount of heat supplied to a reversible engine at temperature T and the heat is rejected to the sink at the dead state T_o. The maximum work obtained, or exergy is:

\(X = {W_{max}} = \left( {1 - \frac{{{T_o}}}{T}} \right)Q = \left( {\frac{{T - {T_o}}}{T}} \right)Q\)

It means that only \(1 - \frac{{{T_o}}}{{{T}}} \) fraction of the Q is available heat.

For a given Q and T: Wmax ∝ T – T0

That is, as T – T0 increases, availability increases.

Calculation:

T = 927°C = 1200 K

T_o = 27°C = 300 K