F.4 Physics

Your argument:
Energy lost = Energy absorb
0.5(334000)+0.5(4200)(T-0)=0.3(4200)(75-T)

The question already states that there is ice remained. But in your equation, you assume ALL 0.5 kg of ice has been melted. This is the mistake.

The answer to the first part of the question is simple. It is given that there is ice remained, the final temperature of the mixture must be 0'C, as ice and water are in thermal equilibrium. You don't need to do any calculation at all. Just answer the question by argument.

To answer the second part of the question, just assume m be the mass of ice remained, then the heat balance equation becomes:

(0.5-m).(334000) =0.3(4200)(75)
solve for m gives m = 0.217 kg

i still do not know how to do, especially How much ice remained?

上次的意見欄：
https://hk.knowledge.yahoo.com/question/question?qid=7015042300022

2015-06-13 21:47:11 補充：
你回應得那麼快？？

你要先明白，兩堆物件處於兩個狀態，一個是75°C的水，一個是0°C的冰。

不同溫度的物件放在一起，在 equilibrium 的時候，溫度必需相同。

因此，我們要留意兩者之間的不同階段：

75°C 的水
74°C 的水
73°C 的水
‧‧‧
1°C 的水
0°C 的水
0°C 的冰

2015-06-13 21:48:41 補充：
今次主要要看三個狀態：

75°C 的水 ＜－－－－＞ 0°C 的水 ＜－－－－＞ 0°C 的冰

　　　　看 heat capacity　　　　　看 latent heat

2015-06-13 21:55:54 補充：
（75°C 的水⇒ 0°C 的水）釋放出 94500 J

於是
（0°C 的冰 ⇒ 0°C 的水）接收了 94500 J

留意 94500 J 並不能把所有冰變作水，所以可以用前邊的方法計算可以知道剩下多少冰。


額外思考：
如果 hot water 不是 0.3 kg，而是 3 kg，那麼最後的結果不單止可以把所有冰溶掉，而且最終的溫度也不是 0°C，而是較高的溫度，設為 x°C，那麼：
(3)(75 - x)(4200) = (0.5)(334000) + (0.5)(x - 0)(4200)
得出 x = 52.9252
最終溫度 = 52.9252°C

2015-06-14 16:15:44 補充：
天同知識長的答案比較精簡，我把我的答案移過來這一邊吧。
(◕‿◕✿)

Assume that for water the specific heat capacity is 4200 J/kg/°C and the specific latent heat of fusion is 334000 J/kg.

For the 0.3 kg of hot water at 75°C to drop to 0°C, the heat energy released is
(0.3)(75 - 0)(4200) = 94500J.

2015-06-14 16:15:55 補充：
For the 0.5 kg of ice at 0°C, the total latent heat of fusion (i.e. the total energy needed to melt them all) is
(0.5)(334000) = 167000J.

Therefore, the 0.3 kg of hot water at 75°C does not have enough heat energy to melt all the ice.

The final temperature of the mixture is 0°C.

2015-06-14 16:16:09 補充：
94500J can melt 94500/334000 = 0.282934132 kg of ice.

Therefore, the mass of ice remained is
0.5 - 0.282934132 = 0.217065868 kg.

2015-06-14 16:16:23 補充：
回應補充發問：

不正確，因為你的公式只適用於 T > 0。
［原意是若有很多熱水，那不單止可以溶冰，也可以提升水溫。］
［請看看意見欄我提出的例子。］

但你得出 T < 0，可見情況不合用。
所以要再進一步思考，得知原來 0.3 kg 75°C 的水並未能把所有冰溶掉，因此最終溫度是 0°C。