what would be the final temperature when 80kg of 0 degrees C cold water is mixed with 60kg of 40 degrees C warm water.
The sum of the heats gained is zero (one of them loses heat, or negative heat gained).
Heatgained80 + heatgained60=0
80*c*(Tf-0) + 60*c*(Tf-40)=0
solve for Tf.
To find the final temperature when mixing two substances, we can use the principle of conservation of energy. According to this principle, the heat gained by one substance must be equal to the heat lost by the other substance.
In this case, we have two substances: 80kg of cold water with an initial temperature of 0°C, and 60kg of warm water with an initial temperature of 40°C. Let's assume the final temperature of the mixture is Tf.
We can calculate the heat gained by the cold water using the formula:
Heatgained80 = mass80 * specific heat capacity * (Tf - initial temperature)
Heatgained80 = 80kg * specific heat capacity * (Tf - 0°C)
Similarly, we can calculate the heat gained by the warm water using the formula:
Heatgained60 = mass60 * specific heat capacity * (Tf - initial temperature)
Heatgained60 = 60kg * specific heat capacity * (Tf - 40°C)
According to the principle of conservation of energy, the sum of the heats gained by the two substances should be zero. Therefore, we can set up the following equation:
Heatgained80 + Heatgained60 = 0
80 * specific heat capacity * (Tf - 0°C) + 60 * specific heat capacity * (Tf - 40°C) = 0
Now, we can solve this equation to find the final temperature Tf. Rearranging the equation gives:
80 * (Tf - 0°C) + 60 * (Tf - 40°C) = 0
Multiplying out the terms:
80Tf - 0 + 60Tf - 2400 = 0
Combining like terms:
140Tf - 2400 = 0
Adding 2400 to both sides:
140Tf = 2400
Dividing by 140:
Tf = 2400 / 140
Simplifying:
Tf ≈ 17.14°C
Therefore, the final temperature of the mixture would be approximately 17.14°C.