To solve this problem, we can use the principle of conservation of energy. The total energy of the hot water entering the system must be equal to the total energy of the final bath water.
Let's denote the initial temperature of the bath water as Tb. The energy gained by the hot water entering the bath is given by:
Q_hot = m_hot * c * (T_hot - Tb)
Similarly, the energy gained by the cold water entering the bath is given by:
Q_cold = m_cold * c * (T_cold - Tb)
Since the total energy gained by the system should be equal to zero (energy is conserved), we have:
Q_hot + Q_cold = 0
Substitute the given values into the equations:
8 * c * (85 - Tb) + 20 * c * (30 - Tb) = 0
8 * 85 - 8Tb + 20 * 30 - 20Tb = 0
680 - 8Tb + 600 - 20Tb = 0
1280 - 28Tb = 0
28Tb = 1280
Tb = 1280 / 28
Tb ≈ 45.71⁰C
Therefore, the initial temperature of the bath water was approximately 45.71⁰C. This is the final temperature of the bath water after 5 minutes of running both taps.
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
1 answer
1 answer