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In an electrically heated boiler, water is boiled at 140°C by a 90 cm long, 8 mm diameter horizontal heating element immersed in water. The heating element is made of mechanically polished stainless steel. The boiler initially contains 0.25 m of water at 20°C. Once boiling starts, it is observed that 25% of the water in the boiler evaporated in 60 min. i. Determine the power rating of the electric heating element immersed in water and the surface temperature of the heating element. [8 marks] ii. Using the above heater, estimate the time required to raise the temperature of 0.25 m2 of cold water from 20°C to 140°C

User Gurkenglas
by
7.9k points

1 Answer

3 votes

Step-by-step explanation:

The given data is as follows.

Volume of water = 0.25
m^(3)

Density of water = 1000
kg/m^(3)

Therefore, mass of water = Density × Volume

=
1000 kg/m^(3) * 0.25 m^(3)

= 250 kg

Initial Temperature of water (
T_(1)) =
20^(o)C

Final temperature of water =
140^(o)C

Heat of vaporization of water (
dH_(v)) at
140^(o)C is 2133 kJ/kg

Specific heat capacity of water = 4.184 kJ/kg/K

As 25% of water got evaporated at its boiling point (
140^(o)C) in 60 min.

Therefore, amount of water evaporated = 0.25 × 250 (kg) = 62.5 kg

Heat required to evaporate = Amount of water evapotaed × Heat of vaporization

= 62.5 (kg) × 2133 (kJ/kg)

=
133.3 * 10^(3) kJ

All this heat was supplied in 60 min = 60(min) × 60(sec/min) = 3600 sec

Therefore, heat supplied per unit time = Heat required/time =
(133.3 * 10^(3)kJ)/(3600 s) = 37 kJ/s or kW

The power rating of electric heating element is 37 kW.

Hence, heat required to raise the temperature from
20^(o)C to
140^(o)C of 250 kg of water = Mass of water × specific heat capacity × (140 - 20)

= 250 (kg) × 40184 (kJ/kg/K) × (140 - 20) (K)

= 125520 kJ

Time required = Heat required / Power rating

=
(125520)/(37)

= 3392 sec

Time required to raise the temperature from
20^(o)C to
140^(o)C of 0.25
m^(3) water is calculated as follows.


(3392 sec)/(60 sec/min)

= 56 min

Thus, we can conclude that the time required to raise the temperature is 56 min.

User Arshin
by
8.4k points
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