What would be the final temp when 100 kg of 0 degrees Celcius cold water is mixed with 60 kg of 35 degrees warm water?
Ans is in degrees Celcius.
The sum of the heats gained is zero (remember one will lose heat, so have a negative heat gained).
Heatgained by cold water + heat gained by hot water=0
100kg*c*(finaltemp-0)+ 60kg*c*(finaltemp-35)=0
solve for final temp. Notice the specific heat c divides out.
To find the final temperature when two substances are mixed, we can use the principle of conservation of energy. The total heat gained by one substance is equal to the total heat lost by the other substance.
Let's assume the final temperature of the mixture is 'T' degrees Celsius.
According to the principle of conservation of energy:
Heat gained by the cold water + Heat gained by the warm water = 0
The heat gained by the cold water can be calculated using the formula:
Heat gained by cold water = mass of cold water * specific heat capacity * (final temperature - initial temperature)
In this case, the mass of the cold water is 100 kg, the specific heat capacity is denoted by 'c', the initial temperature is 0 degrees Celsius, and the final temperature is 'T' degrees Celsius. So, the heat gained by the cold water is:
Heat gained by cold water = 100 kg * c * (T - 0)
Similarly, the heat gained by the warm water can be calculated using the formula:
Heat gained by warm water = mass of warm water * specific heat capacity * (final temperature - initial temperature)
Given that the mass of the warm water is 60 kg, the specific heat capacity is 'c', the initial temperature is 35 degrees Celsius, and the final temperature is 'T' degrees Celsius. So, the heat gained by the warm water is:
Heat gained by warm water = 60 kg * c * (T - 35)
Now, equating the two equations and simplifying:
100 kg * c * (T - 0) + 60 kg * c * (T - 35) = 0
Solving this equation will give us the final temperature 'T'.
Please note that the specific heat capacity (c) will cancel out from both sides of the equation, so we don't need to know its specific value to find the final temperature.