Mix steam with colder water, what is final temp?

Anyways, the summary of the conversation is that 100 g of steam at 100C is mixed with 1 kg of water at 10C, and the final temperature of the mixture is being calculated using the heat capacity of water (4.186 kJ kg-1 K−1), latent heat of vaporization for water (2256 kJ kg−1), and latent heat of fusion for water (334 kJ kg−1). The calculation involves a phase change from steam to water, followed by energy exchange between the two substances until they reach the same temperature. The calculation yields a final temperature of 60C, which is different from the correct answer of 67C.
  • #1
SunshineCat
4
0

Homework Statement


100 g of steam at 100C is mixed with 1 kg of water at 10C. What is the final temperature of the mixture? (in C)
heat capacity of water: cw = 4.186 kJ kg-1 K−1
latent heat of vapourisation for water: Lv = 2256 kJ kg−1
latent heat of fusion for water: Lf = 334 kJ kg−1

Homework Equations


Q=mL
Q=mcΔT

The Attempt at a Solution


I think that there needs to be a phase change of condensation, 0.1kg of 100C steam to 0.1kg of 100C water, so this will be Q=mL and will be an energy loss
The energy lost will go to the colder water
After this, energy will keep flowing from the 100C water to 10C water until they reach the same temperature, energy gain and loss will be Q=mcΔT
I can't seem to get the calculation right, I keep getting 60C when the answer is 67C

ΔQ (steam) = ΔQ(water)
Q=mcΔT = mL + mcΔT
0.1x4.186x(T-100) = 1x4.186x(T-10) - 0.1x225.6
225.6=3.77T
T=60C?
 
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  • #2
SunshineCat said:
0.1x4.186x(T-100) = 1x4.186x(T-10) - 0.1x225.6

That should be 0.1 * 2256
 
  • #3
CWatters said:
That should be 0.1 * 2256
Oh yeah, that was a typo I think
 

FAQ: Mix steam with colder water, what is final temp?

1. What happens when you mix steam with colder water?

When steam and colder water are mixed, the steam will condense into liquid water as it loses heat energy to the colder water.

2. What determines the final temperature when mixing steam with colder water?

The final temperature when mixing steam with colder water is determined by the initial temperature and amount of both the steam and colder water. The specific heat capacities of the substances also play a role in the final temperature.

3. Is the final temperature of a mixture of steam and colder water always higher than the temperature of the colder water?

No, the final temperature of a mixture of steam and colder water may be lower than the temperature of the colder water if the amount of steam is significantly less than the amount of colder water or if the initial temperature of the steam is significantly lower than the initial temperature of the colder water.

4. Can the final temperature of a mixture of steam and colder water be calculated?

Yes, the final temperature of a mixture of steam and colder water can be calculated using the formula Q = mCΔT, where Q is the heat lost or gained, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.

5. Why is mixing steam with colder water important in certain industrial processes?

Mixing steam with colder water can be important in certain industrial processes because it allows for precise control of the final temperature of the mixture. This can be useful in processes that require a specific temperature for optimal results, such as in chemical reactions or in steam-powered machinery.

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