please help An electrical heater is used to heat 1 liter of water from 14 degree

Question

please help

An electrical heater is used to heat 1 liter of water from 14 degree C to the boiling temperature at atmospheric pressure. Derive an expression for the water temperature as a function of time If heater delivers 1000 W to the water, how long does it take until the boiling temperature I reached? Without neglecting heat losses to the environment, and the heat capacities of the heating element and the container. Data: Mass of heater and container = m_b = 400 g Specific heal capacity of heater and container C_pk = 0.5 kJ kg^-1 K^-1 Specific heal capacity of water = C_pv = - 4200 kg^-1 K^-1 Surface area of container = A = 0.1 m^2 Ambient air temperature = T_c = 20 degree C? Overall heal transfer coefficient

Explanation / Answer

Mass of 1litre of water = 1 kg

1000 W = 1 joules / second

1 g of water needs 4.184 J to raise the temperature by 1oC

water temperature = 14oC

Heat required (J) = Mass of water * Change in temperature x 4.184 J/oC g

Change in temperature = 100 - 14 = 86 0C

Heat required (J) = 1000 g * 86 oC * 4.184 J/oC g = 359824 J

Time take = 359824J / 1000 J per sec = 359.82 sec

359.82 / 60 = 6 mins

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