Would anyone be able to help me calculate the following questions? I have the answers, I just want to understand the process. If you are able to give me any feedback, would you be able to write your answer in simple steps plugging in the values? Thank you.
I'm not demanding answers and if it seems that way, I'm sorry! I really do just want to understand HOW to get to the answers (no matter what values I'd plug into the equation).
Steam at 100 °C is mixed with 191.2 g of ice at – 44.1 °C, in a thermally insulated container, to produce water at 53.2 °C. Ignore any heat absorption by the container.
How much energy is required to bring all the ice up to 0 °C? ANSWER: 17600.0 J
How much energy is required to melt the ice into water at 0 °C? ANSWER: 63700.0 J
How much energy is required to raise the temperature of this melted water to its final temperature (53.2 °C).ANSWER: 42600.0 J
How much energy must then be supplied by the steam to change the state of 191.2 g of ice at –44.1 °C to water at 53.2 °C? ANSWER: 124000.0 J
What is the final mass of water in the cup at 53.2 °C? ANSWER: 242.0 g
The amount of energy required to change the temperature of a substance of: mass $ M $, specific heat $S$ is given by $$\text{Energy} = MS\Delta T$$ where $\Delta T$ is the change in temperature that the substance undergoes. This equation holds good only if the substance doesn't change its phase (solid to liquid or liquid to gas etc). In your first question, the ice is initially at $ -44.1^\circ $ C and then goes to $ 0^\circ $C (still being ice at $ 0^\circ $). You know the mass of the ice, you can find out the specific heat from some science data book (it should be mentioned in the question ideally). $$ $$ Here, the mass is given to be $ 191.2 $g and $\Delta T = 44.1^\circ = 44.1 K$. The specific heat of ice is $ 2.11 J \cdot g^{-1} \cdot K^{-1} $ So, the energy that must be supplied is $$ (191.2)\cdot(2.11)\cdot(44.1) \approx 17800 \, J$$ The difference in the answers is because the value of specific heat that the book-author has used is $\approx 2.08$ I used the one available on wikipedia.
If a substance undergoes phase transition, (solid to liquid or liquid to gas or vice versa), then the amount of energy required/given out is given by the expression: $$ \text{Energy} = ML $$ where $L$ is the latent heat of fusion or vapourisation depending upon the process involved. That should be given in the question statement or in the data book. $$ $$ Here,the phase transition is from solid to liquid. So, we must use the latent heat of fusion. Wikipedia says that for water, the latent heat of fusion is $ 334 \text{ kJ/kg} = 334 \text{ J/g } $. So, using the equation, we get the energy required as: $$ (191.2) \cdot (334) \approx 63800 \,J $$
Pretty much the same as the first part of the problem.
Pretty much the same as the second part of the problem.
However, I'd like to know why you had to ask this - after all, all this information should've been explained nicely in your textbook - in much greater depth than what I have presented here, with examples and stuff. Did you give a read to the textbook? If you did and didn't understand, then that's fine. But I wouldn't appreciate not reading the text and straight away asking the question here. (I've done that before and since someone pointed out, I always research before asking).