Formula: final temperature when mixing water with water

In summary, the conversation discusses how to find the final temperature when mixing two different amounts of water with different temperatures. The equation used is (m1*C1*tf)+(m2*C2*tf)=(m1*C1*t1)+(m2*C2*t2). The specific heat capacity of water is also mentioned as a factor in the equation.
  • #1
Sanne
1
0
Back to basics - sorry, my class doesn't have a textbook or the like.

Can one of you nice people please tell me: the formula for the final temperature when mixing two different amounts of water of different temperatures?

If it's complicated you're of course welcome to explain ;)
 
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  • #2
You could always derive it for yourself. Start by considering the equation of the specific heat capacity.
 
  • #3
To find the temperature of water mixed with water in a calorimeter you can use this equation.

Temperature[final] = (Mass[1]*Heat specific[1]*Temperature[1]+Mass[2]*Heat specific[2]*Temperature[2])/(Mass[1]*Heat specific[1]+Mass[2]*Heat specific[2])

EXAMPLE:

1: 1 kilo gram of water at 20 degrees Celsius.
2: 0.3 kilo gram of water at 9 degrees Celsius
The heat specific of water is 4182.

(1*4182*20+0.3*4182*9c)/(1*4182+0.3*4182) = 17.461 Degrees Celsius.

-Eskild.
 
  • #4
because your adding the two different masses of water together the equation:
q1+q2=0 where q1 is the first amount of water at t1 and q2 is the second amount of water at t2. We need to state that the final temp is tf. the value is 0 because the system neither gains nor looses heat.

If you expand the equation you get:
m1C1(tf-t1)+m2C2(tf-t2)=0

expanding further we get:
[(m1*C1*tf)-(m1*C1*t1)+(m2*C2*tf)-(m2*C2*t2)]=0
rearranging:
(m1*C1*tf)+(m2*C2*tf)=(m1*C1*t1)+(m2*C2*t2)

now solve for the item you need.
 
Last edited:
  • #5
hootenanny youre such a dick, answer the question and just give the equation, your comment is so helpful
 
  • #6
deex91 said:
hootenanny youre such a dick, answer the question and just give the equation, your comment is so helpful

Responding with vitriol to a post that was made in 2006 (and which was perfectly in line with forum policy) is not an auspicious beginning to your posting career, deex91!
 

1. What is the formula for calculating the final temperature when mixing water with water?

The formula for calculating the final temperature when mixing water with water is Tf = (m1T1 + m2T2)/(m1 + m2), where Tf is the final temperature, m1 and m2 are the masses of the two water samples, and T1 and T2 are their respective initial temperatures.

2. What units should be used for the masses and temperatures in the formula?

The masses should be in grams (g) and the temperatures should be in degrees Celsius (°C).

3. Can this formula be used for any amount of water?

Yes, this formula can be used for any amount of water as long as the masses and temperatures are given in the correct units.

4. How accurate is this formula?

This formula is highly accurate for ideal situations, where there is no heat lost to the surroundings or energy transferred to or from other objects. However, in real-world scenarios, there may be some slight variations due to external factors.

5. Are there any limitations to using this formula?

Some limitations to using this formula include assuming that the water samples are the same temperature to begin with, neglecting any energy transfer to or from other objects, and not taking into account any phase changes that may occur during the mixing process.

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