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Given 100g of steam at 150 degrees, how much heat will you have to absorb from the system to have 100g of ice as a result?

I know that we need m * q * dT kJ to increase of dT the temperature of an object of mass m and specific heat q, and how much energy it is necessary for a certain material to go from a state to another; yet the numbers do not add up.

Any heads up on the matter? Thank you.

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    $\begingroup$ 100g of steam at 150 C (?) is insufficient information. Is it saturated steam? Superheated steam? What is the pressure? $\endgroup$ – Bob D Dec 16 '18 at 17:58
  • $\begingroup$ Doubt that there is a specific formula for this. I think you'll have to do it piece wise. So how much heat to melt 100 g of ice at 0C to water at 0C. How much heat to take 100 g of water from 0 to 100C. How much heat to evaporate 100 g of water. Finally how much heat to take 100 g steam at 100C to 150 C. $\endgroup$ – MaxW Dec 16 '18 at 17:59
  • $\begingroup$ @MaxW Exactly how I went about solving this; it doesn't add up however. The resulting energy should be 0,31MJ. $\endgroup$ – Fehniix Dec 16 '18 at 18:07
  • $\begingroup$ You need to know the pressure of the steam. Also, need to know if process is at constant $P$ or something different. Assuming you know $P$ and it is constant: find the heat to produce sat'ed steam at given $P$; find the heat to produce sat'ed liquid; find the heat to cool liquid to 0°; find heat to produce ice; add them up. $\endgroup$ – Themis Dec 16 '18 at 18:19
  • $\begingroup$ @MaxW: Are you assuming the steam in the problem is at 1 atm? This is not given in the problem statement. $\endgroup$ – Themis Dec 16 '18 at 18:21
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OK so you say the pressure is 1 atmosphere. Since the boiling temperature of water is 100 C at one atmosphere, then your 150 C steam must be superheated steam at 1 atmosphere.

Now you can apply your specific heat equation to determine how much heat must be removed to reduce the temperature of superheated steam at 150 C, 1 atm., to saturated steam at 100 C, 1 atm. You will need an appropriate value(s) of $C_p$ for water vapor in the range 100 C – 150 C at 1 atm.

You will now have saturated water vapor at 100 C and 1 atm. You can the look up the specific enthalpy (kJ/kg) in the saturated steam table. Then you can calculate the heat removed in order to convert saturated vapor to saturated liquid.

Now you will again apply your specific heat equation to reduce the temperature from 100 C saturated liquid at 1 atm to to 0 C water at 1 atm.

Finally use the latent heat of fusion to convert the 100 g of water at 0C to 100 g of ice at 0 C.

Hope this helps.

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