To calculate the final temperature of the bath water, we can use the principle of conservation of energy.
The total heat gained by the bath water is equal to the heat lost by the hot water and cold water entering the bath.
Heat lost by the hot water = mass * specific heat capacity * (initial temperature - final temperature)
= 8kg * 4186 J/kg°C * (85°C - Tf)
Heat lost by the cold water = mass * specific heat capacity * (initial temperature - final temperature)
= 20kg * 4186 J/kg°C * (Tf - 30°C)
Since the total heat gained is equal to the total heat lost:
8kg * 4186 J/kg°C * (85°C - Tf) = 20kg * 4186 J/kg°C * (Tf - 30°C)
Solving for Tf:
8 * 4186 * (85 - Tf) = 20 * 4186 * (Tf - 30)
33488(85 - Tf) = 83720(Tf - 30)
284080 - 33488Tf = 83720Tf - 2511600
33488Tf + 83720Tf = 284080 + 2511600
117208Tf = 2795680
Tf = 2795680 / 117208
Tf = 23.85°C
Adding 273.15 to convert to Kelvin:
Tf = 297.0 K
Therefore, the final temperature of the bath water after 5 minutes will be 297.0 Kelvin.
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 o f the bath water in kelvin's, ignoring heat loses to the surrounding. In kelvin's
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