To find the final temperature of the bath water, we can use the principle of conservation of energy (specifically, the principle that the heat lost by the hot water equals the heat gained by the cold water).
Step 1: Determine the initial energy of the hot and cold water:
The specific heat capacity of water is approximately 4.18 J/g∙°C.
Initial energy of hot water = mass × specific heat capacity × change in temperature
= 8kg × 4.18 J/g∙°C × (85°C - final temperature)
= 334.4(85 - final temperature) J
Initial energy of cold water = mass × specific heat capacity × change in temperature
= 20kg × 4.18 J/g∙°C × (final temperature - 30°C)
= 83.6(final temperature - 30) J
Step 2: Set up the equation based on the conservation of energy principle:
Initial energy of hot water = Final energy of hot water + Final energy of cold water
334.4(85 - final temperature) = 334.4(final temperature - 30) + 83.6(final temperature - 30)
Step 3: Solve for the final temperature:
334.4(85 - final temperature) = 334.4(final temperature - 30) + 83.6(final temperature - 30)
28,424 - 334.4final temperature = 334.4final temperature - 10,320 + 83.6final temperature - 2,508
28,424 = 402.4final temperature + 10,188
18,236 = 402.4final temperature
final temperature ≈ 45.4°C
Therefore, the final temperature of the bath water after the hot and cold water have mixed for 5 minutes would be approximately 45.4°C.
A hot water tap of a bath delivers water at 85⁰C at a rate of 8kg per minute. The cold tap at the bath delivers water at 30⁰C at the rate of 20kg per minute. If both tapes are at a time of 5 minutes. Calculate the final temperature of the bath water, ignoring heat loss to the surrounding in kelvin's .
Explain vividly step by step
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