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15 kg of water is heated in an insulated tank by a churning process from 300 K to 340 K. If the surrounding temperature is 300 K, find the loss in availability for the process.

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Mass of water, m = 15 kg 

Temperature, T1 = 340 K

Surrounding temperature, T0 = 300 K 

Specific heat of water, cp = 4.187 kJ/kg K 

Loss in availability : 

Work added during churning  = Increase in enthalpy of the water 

= 15 × 4.187 × (340 – 300) = 2512.2 kJ 

Now the energy in the water = 2512.2 kJ 

The availability out of this energy is given by

m[(u1 – u0) – T0 ∆s]

∆s = cp loge\(\left(\cfrac{T_1}{T_0}\right)\)

∴ ∆s = 4.187 loge \(\left(\cfrac{340}{300}\right)\) = 0.524 kJ/kg K

∴ Available energy

= m [cv (T1 – T0) – T0 ∆s] 

= 15 [4.187 (340 – 300) – 300 × 0.524] = 158.7 kJ

∴ Loss in availability

= 2508 – 158.7 = 2349.3 kJ.

This shows that conversion of work into heat is highly irreversible process (since out of 2512.2 kJ of work energy supplied to increase the temperature, only 158.7 kJ will be available again for conversion into work).

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