Question
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 in kelvin's, ignoring heat loses to the surrounding.
Answers
GPT 3.5
To find the final temperature of the combined water, we can use the principle of conservation of energy.
Consider the heat gained by the hot water = Heat lost by the cold water.
Mass of hot water (m1) = 8 kg
Initial temperature of hot water (T1) = 85⁰C = 358 K
Mass of cold water (m2) = 20 kg
Initial temperature of cold water (T2) = 30⁰C = 303 K
Final temperature of the combined water = T_final
Heat gained by the hot water = m1 * c * (T_final - T1)
Heat lost by the cold water = m2 * c * (T_final - T2)
m1 * c * (T_final - T1) = m2 * c * (T_final - T2)
8 * (T_final - 358) = 20 * (T_final - 303)
8T_final - 2864 = 20T_final - 6060
12T_final = 3196
T_final = 266.33 K
Therefore, the final temperature of the combined water after 5 minutes will be approximately 266.33 K.
Consider the heat gained by the hot water = Heat lost by the cold water.
Mass of hot water (m1) = 8 kg
Initial temperature of hot water (T1) = 85⁰C = 358 K
Mass of cold water (m2) = 20 kg
Initial temperature of cold water (T2) = 30⁰C = 303 K
Final temperature of the combined water = T_final
Heat gained by the hot water = m1 * c * (T_final - T1)
Heat lost by the cold water = m2 * c * (T_final - T2)
m1 * c * (T_final - T1) = m2 * c * (T_final - T2)
8 * (T_final - 358) = 20 * (T_final - 303)
8T_final - 2864 = 20T_final - 6060
12T_final = 3196
T_final = 266.33 K
Therefore, the final temperature of the combined water after 5 minutes will be approximately 266.33 K.