Expressions for energy of a closed systems in terms of availability and Thermodynamic second law efficiency

EXPRESSIONS FOR ENERGY OF A CLOSED SYSTEMS IN TERMS OF AVAILABILITY AND SECOND LAW EFFICIENCY

Case (a): Constant volume process

Consider air heated from the temperature of T1 to T2 at constant volume and also heat transfer with the surrounding at To.

Total heat energy supplied to air, Q = m Cv (T2 - T1)

Available energy, A.E = Q - To ΔS

where ΔS = m Cv In (T2 / T1)

Unavailable energy, U.A.E = Q - A.E

U.A.E = m Cv (T2 - T1) - [m Cv (T2 - T1) - To ΔS]

= To ΔS

Case (b): Constant pressure process

If air is heated from T1 to T2 with the surrounding at the temperature of To,

Heat energy supplied, Q = m Cv (T2 - T1)

Available energy, A.E = Q - To ΔS

Where ΔS = m Cp In (T2 / T1)

Unavailable energy, U.A.E = Q - A.E

U.A.E = m Cp (T2 - T1) - [m Cp (T2 - T1) - To ΔS] = To ΔS

Case (c): Constant temperature or isothermal process

Heat energy, Q = p1v1 In (p1 / p2)

Available energy, A.E = Q - To ΔS

ΔS = Q/T1 or Q/T2

Unavailable energy, U.A.E = To ΔS

Case (d): Polytropic process