Well you seem to be assuming quite a few things about them so I just thought naturally seeing how you're getting things incorrect I thought maybe some education was in order. :P
It doesn't matter even if I'm assuming anything wrong about penguins. As if I care. 😈
Q-100g ice at 0C is mixed with 10g steam at 100C. Find the final temperature and composition.
How to solve?
Use the following equation to determine the amount of energy required to melt the ice. Q = mass * Hf = 3.36 * 10^5 J
Use the following equation to determine the amount of energy required to increase the temperature of water from 0 to 100.
Q = mass * Specific heat * ∆T Specific heat = 4186 J/(kg * ˚C) Q = 1 * 4186 * 100 = 418,600 J Total energy required = 3.36 * 10^5 + 418,600 = 7.546 * 10^5 J
This is the amount of energy that is required to melt the ice and increase the temperature of the water to 100˚C. Lets use this number in the following equation to determine the amount of steam that it will condense.
Q = mass * H vap = 2.26 * 10^6 J 7.546 * 10^5 = mass * 2.26 * 10^6 Mass = 7.546 * 10^5 2.26 * 10^6 = 0.333893805 kg
This is approximately 0.334 kg. This means all of the steam didn't condense. To determine the mass of steam that didn't condense, subtract this number from 1kg. The mass is approximately 0.666 kg.