# Heat required to heat water and ice

• Elias Waranoi
In summary, the conversation discusses the question of whether the answer in a physics book is incorrect or if something was missed in regards to a problem involving a thermally insulated vessel containing water and ice, with a tube leading from a boiling boiler inserted into the water. The question asks for the amount of steam needed to condense in order to raise the temperature of the system to 28.0°C, and the conversation provides relevant equations and a solution based on those equations. The final answer is found to be 190 grams, accounting for the error in the physics book.
Elias Waranoi
Is the answer in my physics book wrong or did I miss something?

## Homework Statement

A vessel whose walls are thermally insulated contains 2.40 kg of water and 0.450 kg of ice, all at 0.0°C. The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water. How many grams of steam must condense inside the vessel (also at atmospheric pressure) to raise the temperature of the system to 28.0°C? You can ignore the heat transferred to the container.

mw = 2.4 kg
mi = 0.45 kg
ΔT = 28 C°
c = 4190
Lf 334 * 10^3 J/kg
Lv 2256 * 10^3 J/kg

Q = mcΔT
Q = ±mL

## The Attempt at a Solution

Heat required to melt ice and warm water to 28 C°:
Qreq = miLf + (mi + mw)cΔT

Condensing steam of amount Qreq = -msLv
ms = -(miLf + (mi + mw)cΔT)/Lv
ms = -215 grams

My physics book tells me the answer is 190 grams, which I get if I don't account for mi in (mi + mw)cΔT. This seems wrong to me but I wanted to ask and make sure, every other time I've claimed that I found an error in my physics book I have been incorrect.

When the steam condenses, is it at the final temperature?

Oops, thank you I got it right now.

## 1. How much heat is required to melt ice into water?

The amount of heat required to melt ice into water is known as the heat of fusion. It takes 334 joules of energy to melt 1 gram of ice at its melting point of 0 degrees Celsius.

## 2. How much heat is needed to raise the temperature of water?

The amount of heat required to raise the temperature of water depends on the starting temperature of the water and the desired final temperature. It can be calculated using the specific heat capacity of water, which is 4.184 joules per gram per degree Celsius.

## 3. Does it take more heat to heat water or ice?

It takes more heat to heat ice than water because ice has a lower specific heat capacity than water. This means that it requires more energy to raise the temperature of ice compared to water.

## 4. How does the heat required to heat water and ice vary with atmospheric pressure?

Atmospheric pressure does not have a significant effect on the heat required to heat water and ice. The heat of fusion and specific heat capacity of water are not greatly affected by changes in pressure.

## 5. Is it more efficient to heat water or ice?

It is more efficient to heat water because it requires less energy to raise the temperature of water compared to ice. This is due to the higher specific heat capacity of water.

• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
5K
• Introductory Physics Homework Help
Replies
7
Views
8K
• Introductory Physics Homework Help
Replies
2
Views
4K
• Introductory Physics Homework Help
Replies
7
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
4K