A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.
Given: The base area of brass boiler is 0 .15 m 2 , its thickness is 1 .0 cm and the rate at which it boils water is 6.0 kgmin − 1 .
The amount of heat flowing into water is given as,
θ = K A ( T 1 − T 2 ) t l (1)
Where, base area of the boiler is A , thickness of the boiler is l , time taken to boil unit mass of water is t , temperature of flame is T 1 and temperature of boiling water is T 2 .
Heat required for boiling water is given as,
θ = m L (2)
Where, m is the mass of water and L is the heat of vaporization of water.
From equations (1) and (2), we get
m L = K A ( T 1 − T 2 ) t l T 1 − T 2 = m L l k A t
By substituting the given values in the above expression, we get
T 1 − T 2 = 6 × 2256 × 10 3 × 0.01 109 × 0.15 × 60 T 1 = 138 + 100 = 238 ° C
Thus, the temperature of the part of the flame in contact with the boiler is 238 ° C .
Given: The base area of brass boiler is
The amount of heat flowing into water is given as,
Where, base area of the boiler is
Heat required for boiling water is given as,
Where,
From equations (1) and (2), we get
By substituting the given values in the above expression, we get
Thus, the temperature of the part of the flame in contact with the boiler is
