To find the final temperature of the mixed water, we can use the principle of conservation of energy, where the heat lost by the hot water equals the heat gained by the cold water.
Let's denote:
m1 = mass of hot water = 8 kg/minute * 5 minutes = 40 kg
T1 = initial temperature of hot water = 85°C = 358 K
m2 = mass of cold water = 20 kg/minute * 5 minutes = 100 kg
T2 = initial temperature of cold water = 30°C = 303 K
Tf = final temperature of the mixture (unknown)
Using the principle of conservation of energy, we have:
m1 * Cp * (Tf - T1) = -m2 * Cp * (Tf - T2)
Where:
Cp = specific heat capacity of water = 4186 J/kg*K
Substitute the values and solve for Tf:
40 * 4186 * (Tf - 358) = -100 * 4186 * (Tf - 303)
167440 * Tf - 15095280 = -418600 * Tf + 12638600
586040 * Tf = 27733880
Tf = 27733880 / 586040 = 47.384 K
The final temperature of the mixed water is approximately 47.384°C.
A hot water tap of a bath delivers water at 85⁰C at a rate of 8Kg per minute .the cold water tap at the bath delivers water at 30⁰C at the rate of 20kg per minute. If both tapes are at a time is 5 minute. Calculate the final temperature if both water, ignoring heat loses to the surrounding in kelvin's
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