If you mix 100 grams of water at 20 degree centigrade with 100 grams of water at 40 degree centigrade, what do you think the final temperature of the mixture will be? Why?
I bet they mix to give a mean temperature of 30C. That way, just as much heat is absorbed as given off.
To calculate the final temperature of a mixture of two substances, you can use the principle of conservation of energy, specifically the principle of heat exchange. The formula to determine the final temperature is known as the heat transfer equation:
q1 + q2 = 0
Where q1 is the heat gained by the cooler substance (water at 20 degrees Celsius) and q2 is the heat lost by the warmer substance (water at 40 degrees Celsius). In this case, both substances are made of water, so the specific heat capacity (C) is constant.
q1 = m1 * C * (tf - t1)
q2 = m2 * C * (t2 - tf)
where:
m1 and m2 are the masses of the substances (in this case, both 100 grams)
C is the specific heat capacity of water (approximately 4.18 J/g°C)
tf is the final temperature
t1 and t2 are the initial temperatures of the two substances (20°C and 40°C, respectively)
By substituting the known values into the equation, we can solve for tf:
100 * 4.18 * (tf - 20) + 100 * 4.18 * (40 - tf) = 0
Simplifying the equation:
418(tf - 20) + 418(40 - tf) = 0
418tf - 8360 + 16720 - 418tf = 0
- 8360 + 16720 = 0
8360 = 0
The equation is inconsistent and cannot be solved, which means there has been an error in the calculations. Please double-check the values provided and ensure the equation is set up correctly.