A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is
Entropy change for hot reservoir
Energy gain in cold reservoir
Loss in availability = T0 [ ΔSc + ΔSh ]
⇒ 300(30 – 10)
= 6000 kJ
Availability of a system at any given state is
Availability of system of any given state is when no maximum useful work obtainable as the system goes to dead state.
Considering the relationship TdS = dU + pdV between the entropy (S), internal energy (U), pressure (p), temperature (T) and volume (V), which of the following statements is correct?
The equation is valid for between reversible or inversible process of a closed system. Because it is the relation between properties which are independent to path.
A steel billet of 2000 kg mass is to be cooled from 1250 K to 450 K. The heat released during this process is to be used as a source of energy. The ambient temperature is 303 K and specific heat of steel is 0.5 kJ/kgK. The available energy of this billet is
Heat lost by steel = (0.5)(2000)(450 – 1250)
Gained = 800MJ
ΔSLost by steel = (2000) (0.5)) ln
⇒ –1.021 MJ
(ΔS) gained = 1.021MJ
AE (W) = a – T0dS
= 800 – (303) (1.021)
= 490.7 MJ
The pressure, temperature and velocity of air flowing in pipe are 5 bar, 500 K and 50 m/s, respectively. The specific heats of air at a constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively.Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/ kg of the air stream is
For flow stream,
A.E. =(h2 – h1) + K.E. – T0 (S2 – S1)
= 187 kJ/kg
The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called
Exergy (or) Available Energy :
The maximum portion of energy which could be converted into useful work by ideal processes which reduce the system to dead state (a state in equilibrium with the earth and its atmosphere).