To find the final temperature of the water in the bath after 5 minutes, we can use the principle of conservation of energy.
First, we need to calculate the total amount of heat energy added to the water in the bath from the hot water tap and the cold water tap.
Q_hot = m_hot * c * (T_final - T_hot)
Q_cold = m_cold * c * (T_final - T_cold)
where:
Q_hot = heat energy from the hot water tap (Joules)
Q_cold = heat energy from the cold water tap (Joules)
m_hot = mass of hot water (kg)
m_cold = mass of cold water (kg)
c = specific heat capacity of water (4186 J/kg*K)
T_final = final temperature of water in bath (K)
T_hot = initial temperature of hot water (85°C = 358 K)
T_cold = initial temperature of cold water (30°C = 303 K)
Given:
m_hot = 8 kg/minute * 5 minutes = 40 kg
m_cold = 20 kg/minute * 5 minutes = 100 kg
Now, we can calculate the total heat energy added to the water in the bath:
Q_hot = 40 kg * 4186 J/kg*K * (T_final - 358 K)
Q_cold = 100 kg * 4186 J/kg*K * (T_final - 303 K)
Since the total heat energy added to the water in the bath is conserved:
Q_hot + Q_cold = 0
Substitute the values and solve for T_final:
40 * 4186 * (T_final - 358) + 100 * 4186 * (T_final - 303) = 0
167440(T_final - 358) + 418600(T_final - 303) = 0
167440T_final - 59802180 + 418600T_final - 126616800 = 0
586040T_final = 186418980
T_final = 317.63 K
Therefore, the final temperature of the water in the bath after 5 minutes is 317.63 K.
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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