Steam at 100°C is added to ice at 0°C.
(a) Find the amount of ice melted and the final temperature when the mass of steam is 13 g and the mass of ice is 50 g.
(b) Repeat with steam of mass 3.0 g and ice of mass 50 g.
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There are two ways of doing this
1] Look up the enthalpy [or internal energy] of ice and of steam at conditions specified [though the pressure is not specified above I assume it is one standard atmosphere] in energy per gram [or if in energy/mol convert]
Warning: Make certain the two values are based on the same base temperature !!
2] multiply mass by enthalpy and add --- MiHi + MsHs
3] Divide by total mass to get H on a mass basis
4] Look in the table for what T water has that enthalpy. HOWEVER, you may wind up with a mix of boiling water and steam; for which case you must use a weighted average of BW and steam enthalpies to find proportions
OR
1] Total up the various heats
2] Latent heats are associated with a change in phase
3] 'Sensible' heats go with no phase change; Q = M C DeltaT
4] Calculate the energy required to melt the ice to water at 0C
5] Calculate energy [sensible heat] to bring that water to boiling
6] Calculate energy liberated by condensing the steam to water at 100C
7] Add those energies, watching the signs of 4], 5], and 6] closely
8] If you have energy left over, the product will be a steam/water mix. Divide left over energy by heat of vaporization to see how much stays as steam
9] If you have insufficient energy, then you have water below 100C. Use Q = M C DeltaT to find DeltaT, which will tell you how much below 100 C