Question

3 kg of gas (c_v = 0.81 kJ/kg K) initially at 2.5 bar and 400 K receives 600 kJ of heat from an infinite source at 1200 K. If the surrounding temperature is 290 K, find the loss in available energy due to above heat transfer.

Answer 1

Mass of gas, m_g = 3 kg 

Initial pressure of gas = 2.5 bar 

Initial temperature, T₁′ = 400 K 

Quantity of heat received by gas, Q = 600 kJ 

Specific heat of gas, c_v = 0.81 kJ/kg K 

Surrounding temperature = 290 K 

Temperature of infinite source, T₁ = 1200 K 

Heat received by the gas is given by, 

Q = m_gc_v (T₂′ – T₁′)

600 = 3 × 0.81 (T₂′ – 400)

T₂′ = \(\cfrac{600}{3\times0.81}\) + 400 = 646.9 K say 647 K

Available energy with the source 

= area 1-2-3-4-1 

= (1200 – 290) × \(\cfrac{600}{1200}\) = 455 kJ

Change in entropy of the gas

Unavailability of the gas = area 3′- 4′- 5′- 6′- 3′ 

= 290 × 1.168 = 338.72 kJ

Available energy with the gas 

= 600 – 338.72 = 261.28 kJ 

∴ Loss in available energy due to heat transfer 

= 455 – 261.28 = 193.72 kJ.