[ShadowSpirit]

Sorry, I know this is more physics than chemistry, but I am stuck on this question and I hope someone can help me... (the numbers in {}'s are exponents as I don't know how to type those)

Question: A vessel of heat capacity 126 J/°C contains 0.2 kg of water and 0.02 kg of ice at 0 °C. What would happen if 0.1 kg of steam at 100 °C were passed into the vessel?

Given:
specific latent heat of ice is 3.34 x 10{5} J/kg
specific latent heat of steam is 2.268 x 10 {6} J/kg
specific heat capacity of water is 4200 J/kg/ °C


What I wrote (I assumed the question meant the vessel, water and ice were both at 0 °C, since it seems too complicated otherwise):

Let the final temperature of the mixture be T.

latent heat of steam released + heat loss of steam=heat gain of water + latent heat of ice absorbed + heat gain of ice + heat gain of vessel

2.268 x 10 {6} J/kg x 0.1 kg + 4200 x 0.1 x (100-T) = 4200 x 0.2 x (T-0) + 3.34 x 10{5} x 0.02 + 4200 x 0.02 x (T-0) + 126 x (T-0)

226800 + 42000 - 420T = 840T + 6680 + 84T +126T

262120 = 1470T

T= 178 °C


...Which doesn't makes sense at all. You can't mix something at 100°C and something at 0°C and get a mixture of 178°C... It'd be greatly appreciated if someone can tell me what went wrong with my calculations. Thanks.

[Yggdrasil]

Calculate the heat needed to bring 0.2kg of water and 0.02kg of ice at 0^oC to 100^oC.  How does this compare with the heat released by the condensation of 0.1kg of steam at 100^oC?   What does this tell you about what happens?