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Gases in Liquids

Water flowing...

Question

Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that the specific entropy increases by 2.50 kJ/kg and the specific entropy increases by 0.007 kJ/kgK. the power input to the electric heater is 2.50 kW. There is no other work or heat interaction between the system and the surroundings. Assuming an ambient temperature of 300K, the irreversibility rate of the system is kW. (round off to two decimal places).
2.1

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Solution

The correct option is A 2.1
$h_{2} - h_{1} = 2.50 k J / k g$
$s_{2} - S_{1} = 0.007 k J / k g K$
$I = T_{0} S_{g e n} = 300 \times S_{g e n}$
$S_{g e n} = S_{e x i t} - S_{i n l e t} = (m s_{2}) - (m s_{1} + 0)$
(Entropy associated with work is zero)
$= m (s_{2} - s_{1}) = 1 \times 0.007 = 0.007$
$I = 300 \times 0.007 = 2.10 k W$
Alternate Solution :
$Δ S_{i n i v} = Δ S_{s y s} + Δ S - s u r r = Δ S_{s y s}$
$= m (S_{2} - S_{1}) = 1 (0.0007)$
$Δ S_{i n i v} = 0.007 k W / K$
Irreversibility rate,
$I = T_{0} Δ S_{i n i v} = 300 \times 0.007 = 2.1 k W$

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