To find the final temperature of the water in the bath after 5 minutes, we can use the principle of conservation of energy.
Considering the hot water tap first:
Initial temperature of hot water = 85⁰C
Mass of hot water per minute = 8kg
Time taken = 5 minutes
Energy added by hot water tap = mass x specific heat capacity x change in temperature
= 8 x 4186 x (final temperature - 85)
Now, considering the cold water tap:
Initial temperature of cold water = 30⁰C
Mass of cold water per minute = 20kg
Time taken = 5 minutes
Energy added by cold water tap = mass x specific heat capacity x change in temperature
= 20 x 4186 x (final temperature - 30)
Since the total energy added to the water by both taps will result in an increase in temperature, we can set the two energy equations equal to each other:
8 x 4186 x (final temperature - 85) = 20 x 4186 x (final temperature - 30)
Solving for the final temperature:
8 x (final temperature - 85) = 20 x (final temperature - 30)
8 x final temperature - 680 = 20 x final temperature - 600
12 x final temperature = 80
final temperature = 80 / 12
final temperature ≈ 6.67⁰C
Therefore, the final temperature of the water in the bath, after 5 minutes, would be approximately 6.67⁰C.
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 minutes. If both tapes are at a time of 5 minutes. Calculate the final temperature if the water, ignoring heat loses to the surrounding in kelvin's
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1 answer