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

1 answer

To calculate the final temperature of the water, we can use the principle of conservation of energy, which states that the total energy of the system remains constant.

Let's denote:
m1 = mass of hot water = 8 kg
T1 = initial temperature of hot water = 85⁰C = 85 + 273 = 358 K
m2 = mass of cold water = 20 kg
T2 = initial temperature of cold water = 30⁰C = 30 + 273 = 303 K
Tf = final temperature of the mixture (to be determined)

According to the principle of conservation of energy:
m1 * T1 + m2 * T2 = (m1 + m2) * Tf

Substitute the given values:
8 * 358 + 20 * 303 = (8 + 20) * Tf
2864 + 6060 = 28 * Tf
8924 = 28 * Tf
Tf = 8924 / 28
Tf = 318 K

Therefore, the final temperature of the water mixture is 318 K.