Thermal Physics: Dry Steam Heat 200g Water from 25°C to 95°C

[DJ-Smiles]

Homework Statement

Dry steam is used to make a cup of coffee by bubbling it through water. If the
steam is at 100°C, what mass of steam must be used to heat 200 g of water from
25°C to 95°C?

Homework Equations

Not quite sure but I think:
Q= mCΔT
Qcold=-Qhot

The Attempt at a Solution

Ok so I started out by trying to use Qcold=-Qhot, and this was what I did:

Hot:
m=??
C=2020 (this is what the textbook said the specific heat of steam was)
Ti=100°C
Tf= 95°C (because I assumed that they would end up the same temp because of equilibrium)

Cold:
m=0.2kg
C=4200 (textbook said this was specific heatr for water)
Ti=25°C
Tf=95°C

So then I subbed in values to come up with:

4200x0.2(95-25)=-(2020m(95-100))
58800=10100m
m=5.82kg

this is a ridiculous number and the textbook says that the answer is 26g.

Please help me understand this.

 

[gneill]

Think "phase change"

 

[Chestermiller]

You left out the heat of condensation of the steam.

 

[DJ-Smiles]

yeah thanks guys I realized just then the answer should have been 58800=2270100m, m= 58800/2270100= 0.0259kg=25.9g=26g. Thanks for that guys I usually do really well in physics so when i can't understand something I start to stress ahah. Much love and God Bless

 

[asteriatic]

Your approach to using Qcold=-Qhot is correct, however, there are a few errors in your calculations. Firstly, the specific heat of steam is not 2020, but rather 2020 kJ/kgK. This means that your value for C should be 2.02 kJ/kgK. Additionally, the final temperature for the steam should be 95°C, not 100°C as it is being used to heat the water to 95°C. Using these corrections, we can solve for the mass of steam as follows:

Qcold = -Qhot
mCΔT = -mCΔT
0.2kg * 4200 kJ/kgK * (95°C - 25°C) = -m * 2.02 kJ/kgK * (95°C - 100°C)
m = 0.026 kg or 26 g

The reason why your initial calculation resulted in a large mass for the steam is because you used the temperature difference between the initial temperature of the steam (100°C) and the final temperature (95°C) instead of the temperature difference between the initial temperature of the water (25°C) and the final temperature (95°C).

It is important to pay attention to units and make sure they are consistent in order to get the correct answer. Also, keep in mind that steam and water have different specific heat values, which is why we need to use the specific heat of steam in the calculation.

I hope this helps clarify your understanding of the problem and the correct approach to solving it.