Final temperature of two mixed substances (simply enthelpy math)

However, since the final temperature cannot be higher than both the starting temperatures, you should set the equation up as:100 * (T2 - 100) * 0.385 = 140 * (25 - T2) * 4.185By solving this equation, you will get the final temperature to be 29.6°C.
  • #1
Esoremada
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Homework Statement



A 100-g sample of Cu(s), initially at 100oC, is added to 140 g of water, initially at 25oC. What is the final temperature of the mixture?

Specific heat
(in J g-1 oC-1)
Cu(s) 0.385
H2O(l ) 4.184

Homework Equations



Q = m * ΔT * c

heat lost = heat gained
= m2 * ΔT2 * c2

The Attempt at a Solution



100 * (T2 - 100) * 0.385 = 140 * (T2 - 25) * 4.185
38.5* (T2 - 100) = 585.9 * (T2 - 25)
38.5T2 - 3850 = 585.9T2 - 14647.5
T2 = 19.725°CBut the temperature can't be lower than both their starting temperatures, what did I do wrong? The answer is supposed to be 29.6
 
Last edited:
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  • #2
From the way you have written your equation, you are assuming that the final temperature T2 of the copper is greater than 100 C.
 

1. What is the formula for calculating the final temperature of two mixed substances?

The formula for calculating the final temperature of two mixed substances is Q = mCΔT, where Q is the heat exchanged, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.

2. How does the initial temperature of the substances affect the final temperature?

The initial temperature of the substances will affect the final temperature in the sense that the greater the difference between the initial temperatures, the greater the change in temperature will be. This will result in a higher final temperature.

3. Can the final temperature of two mixed substances ever be lower than the initial temperature of one of the substances?

No, according to the law of conservation of energy, the final temperature of two mixed substances cannot be lower than the initial temperature of one of the substances. Energy is always conserved, so the final temperature will always be between the initial temperatures of the two substances.

4. How does the specific heat capacity of the substances affect the final temperature?

The specific heat capacity of a substance is a measure of how much heat energy is required to raise the temperature of 1 gram of the substance by 1 degree Celsius. The higher the specific heat capacity, the more heat energy the substance can absorb, resulting in a lower final temperature.

5. Is it possible for two substances with the same initial temperature to have a final temperature different from their initial temperature?

Yes, it is possible for two substances with the same initial temperature to have a final temperature different from their initial temperature. This is because the specific heat capacity of the substances may be different, causing one substance to absorb more heat energy and resulting in a different final temperature.

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