Specific and latent heat question

[endeavor]

Steam at 100 degrees Celsius is bubbled into 250 cm³ of water at room temperature in a calorimeter cup. How much steam will have been added when the water in the cup is at 60 degrees Celsius? (Ignore the effect of the cup.)

So I did:
-(Heat lost by steam) = Heat gained by water
m_steamL_vap + m_steamc(40[degrees]C) = m_waterc(40[degrees]C), where c = specific heat of water
solving for m_steam, i get 1.72 * 10^-2 kg.

But the answer is 1.79 * 10^-2 kg. What's wrong with my calculation?

 

[Astronuc]

It appears you are using 20°C for room temperature?

Normally room temperature is 25°C (77°F) is room temperature.

What values did you use for latent heat of vaporization, specific heat of water, and density of water?

 

[endeavor]

I used:
room temperature = 20°C
latent heat of vaporization = 540 kcal/kg
specific heat of water = 1 kcal/kg
density of water = 1g/cm³, so the mass of water = 0.250kg

I just tried 25°C, but it doesn't seem to work...

 

[Hootenanny]

I've always used specific heat in in terms of Joules.

 

[Astronuc]

If one uses the density of water at 1 g/cm³, the one will obtain

m (steam) = 250/(540+40) = 17.2 g or 0.0172 kg.

However, if one corrects for density of water, one will obtain a greater value of the mass of steam.

Density of water at 40°C = 0.9922 g/cc

Density of water at 60°C = 0.9832 g/cc

Density of water at 80°C = 0.9718 g/cc

Density of water at 100°C = 0.958 g/cc.

Using an average value of 0.9922 g/cc for the water heating from 20-60°C and using 0.09718 g/cc for water cooling from 100-60°C, I obtained about 17.6 g or 0.0176 kg of steam.

Here is a reference for water properties -
http://www.thermexcel.com/english/tables/eau_atm.htm (0-100°C)

 

[endeavor]

I've always used specific heat in in terms of Joules.

Yeah, but I thought it'd be easier if I just used kcal because the answer was not going be in terms of heat.

I don't know what my book did, but my answer is close enough for me. Probably what happened was something like you said Astronuc...

 

[sharmeen01]

i am facing problem while understanding the question? Here are my few questions regarding to this particular problem?

What is the importance of room temprature?
I understand only the things from this problem is that 17.2 gram heat is given to the water at 60 degree celsius to make it at 100 degree C steam,
if i am right than what is the importance of room temprature, It's my introduction to thermodynamics so asking such a basic question, with kind regards

 

[sharmeen01]

i am facing problem while understanding the question? Here are my few questions regarding to this particular problem?

What is the importance of room temprature?
I understand only the things from this problem is that 17.2 gram heat is given to the water at 60 degree celsius to make it at 100 degree C steam,
if i am right than what is the importance of room temprature, It's my introduction to thermodynamics so asking such a basic question, with kind regards, waiting for your kind reply.
How one can calculate this problem, becauses there is one thing is in my mind i.e lass of conservation of mass, so what should be the mass of steam at 100 degree Celsius,
Thankyou