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# How to determine the temperature of the transitioning of ice and steam?

If I have ice at -10C and Steam at 120C in a container, what would be the temperature of the water when the two transition from their current states?

If I have ice at -10C and Steam at 120C in a container, what would be the temperature of the water when the two transition from their current states? This question deals with endothermic and exothermic energy use. I need to know how to calculate the temperature of the final product of the transition of ice and steam to water.

### 1 Answer

- billrussell42Lv 72 years agoFavorite Answer
you need quantities of each to solve this. If I assume M = mass of ice and m = mass of steam...

specific heat of water is 4.186 kJ/kgC

specific heat of ice is 2.06 kJ/kgC

specific heat of steam is 2.1 kJ/kgK

heat of fusion of ice is 334 kJ/kg

heat of vaporization of water is 2256 kJ/kg

at then end, the energy required to raise the ice to 0º and melt it and then raise it to the final temp has to equal:

energy to cool the steam to 100º, then condense it, then cool it to the final temp.

Let T be final temp.

in order...

E1 = 2.06 kJ/kgC x M x 10ºC

E2 = 334 kJ/kg x M

E3 = 4.186 kJ/kgC x M x (T–0º)C

and

E4 = 2.1 kJ/kgK x m x (120–100)C

E5 = 2256 kJ/kg x m

E6 = 4.186 kJ/kgC x m x (100–T)C

now

E1 + E2 + E3 = E4 + E5 + E6

plug in numbers and crank your calculator, solve for T

How do you find T?