How many calories of heat is required to convert 1gm of ice at to water at?

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Heat transfer
Specific heat
Latent heat
1. Heating ice
2. Melting ice
3. Heating water
4. Boiling water
5. Heating steam
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Hint: The conversion of ice into steam takes place in three steps: First the ice converts into the water, then the temperature of the water increases to $100^\circ C$ and then the water evaporates to form steam. The amount of heat required to convert $1\ g$ of ice at $0^\circ C$ into steam at $100^\circ C$ is the sum of heat required to convert ice into water, the heat required to raise the temperature from $0^\circ C$ to $100^\circ C$ and then to convert water at $100^\circ C$ into steam.

Complete step by step answer:

Given, Mass of ice to be converted into steam $= 1\ g$Temperature of ice $= 0^\circ C$The heat required to convert ice at $0^\circ C$ into the water at $0^\circ C$ is given as:Mass of ice $\times$ Latent heat of fusion of iceLatent heat of fusion of ice $= 80\ cal/g$Therefore, Heat required to convert ice at $0^\circ C$ into water at $0^\circ C = 1\ g\times 80\ cal/g = 80\ cal$Now, the water at $0^\circ C$ has to be first heated to $100^\circ C$ to be changed into steam.The heat required to raise the temperature of water from $0^\circ C$ to $100^\circ C$ is given as:Mass of water $\times$ Increase in temperature $\times$ Specific heat of waterMass of water is the same as the mass of ice, which is equal to $1\ g$.The increase in temperature of water $= 100^\circ C - 0^\circ C = 100^\circ C$Specific heat of water $= 1\ cal/g^\circ C$Putting all the required values, the heat required to raise the temperature of water $= 1\ g\times 100^\circ C\times 1\ cal/g^\circ C = 100\ cal$After this, further, some heat is required to be supplied to convert the water at $100 ^\circ C$ to steam at the same temperature. The heat required to convert water into steam $=$ Mass of water $\times$ Latent heat of steamMass of water $= 1\ g$The latent heat of steam is given as $536\ cal/g$.Therefore, the heat required $=1\ g\times 536\ cal/g = 536 cal$Now, the total heat required to convert ice to steam $=$ Heat required to convert ice into water $+$ Heat required to raise the temperature to $100^\circ C$ $+$ Heat required to convert water into steam $=80\ cal + 100\ cal + 536\ cal$$=716\ cal$Therefore, the heat required to convert ice at $0^\circ C$ into steam at $100^\circ C$ is equal to $716\ cal$.

So, the correct answer is Option C.

Note: Fusion means melting. So, the latent heat of fusion is defined as the amount of heat required for a solid to melt into a liquid without any temperature rise. Specific heat of any substance is defined as the amount of heat (in calories) required to raise the temperature of one gram of the substance by one degree Celsius.

SfC Home > Physics > Thermal Energy >

by Ron Kurtus

It takes a certain amount of heat energy or thermal energy to turn ice into water and water into steam.

When you heat a material, you are adding thermal kinetic energy to its molecules and usually raising its temperature. The only exception is when the material reaches its melting point or boiling point. At those two temperatures, the heat energy goes into changing the state or phase of the material. After the state has changed, the temperature will rise again with added thermal energy.

The rate temperature changes is the specific heat of the material. The amount of energy required to melt the material is called the latent heat of melting. This all can be illustrated in showing how much heat is required to change ice into water and then change the water into steam.

Questions you may have include:

What units of measurement are used in turning ice into steam?
How is specific heat used?
How is latent heat used?

This lesson will answer those questions. Useful tool: Units Conversion

Since we are measuring the amount of heat required to make these changes, we need to know the definitions of the various units involved.

Heat transfer

Heat is the total kinetic energy of all the molecules in an object. Although energy is typically measured in joules, a more common unit for heat is the calorie, which is defined as the amount of heat required to change the temperature of 1 gram of water by 1 Celsius degree. There is a conversion factor to relate joules to calories, but we won't worry about that here.

Note: Calories are abbreviated as cal and grams as g. Also, oC means degrees Celsius.

In the English measurement system, they use the BTU (British thermal unit), which is the amount of heat required to change the temperature of 1 pound of water by 1 Fahrenheit degree. The BTU is seen in the United States when referring to the capacity of a furnace.

Specific heat

Materials vary in their capacity to store thermal energy. For example, a material like iron will heat up much faster than water or wood. The measurement of how much heat is required to change the temperature of a unit mass of a substance by 1 degree is called its specific heat.

There are charts available listing the specific heat of various materials. The chart below shows the specific heat of ice, water and steam in units of calorie per gram-degree Celsius.

(Note that all items are listed with the same number of decimal points. That indicates the same accuracy for each. Also, the zero in front of the decimal point assures that the reader will know it is a decimal point and not a fly speck.)


Ice	0.50
Water	1.00
Steam	0.48

Specific heat of various states of water

In other words, it would take twice as many calories to heat some water one degree than it would to heat the same mass of ice one degree.

Latent heat

When any material is heated to the temperature where it changes state, the temperature will remain the same until all the material changes state. That means ice water will remain at 0oC (32oF) until all the ice is melted. The same thing applies when cooling the materials.

The reason is that energy must be expended to change the state from solid to liquid or from liquid to gas. Likewise, energy must be withdrawn to change the state when cooling the material. The amount of energy required is call the latent heat of freezing or boiling. The chart below shows the latent heat or energy required to change the states of water.


Melting / Freezing	80
Boiling / Condensation	540

Latent heat required to change state of water

Problem

A good way to understand the concepts is to solve a problem.

Suppose we have 50g of ice at -10oC. We want to heat the material until it all turns to steam at 110oC. How much heat is required?

With a problem that is complex like this one, it is good to break it down into pieces and solve each part individually. This also helps to explain the logic used in the solution.

1. Heating ice

How much heat would be required to raise 50g of ice to its melting point?

The ice temperature must be raised 10 degrees to reach 0oC.

Since the specific heat of ice is 0.50 cal/g-oC, that means that 0.50 calories is needed to raise 1g of ice 1oC. Thus, it would take 50 x 0.50 calories to raise 50g up 1oC and 10 x 50 x 0.50 = 250 cal to raise the ice to its melting point.

2. Melting ice

How much heat would be required to melt the 50g of ice?

The latent heat for melting ice is 80 cal/g. That means that 1g of ice requires 80 cal of heat to melt.

Thus, 50g requires 50 x 80 = 4000 cal to melt.

3. Heating water

How much heat is required to heat 50g of water from 0oC to its boiling point of 100oC?

Since the specific heat of water is 1.00 cal/g-oC, that means that 1.00 calorie is needed to raise 1g of water 1oC. Thus, it would take 50 x 1.00 calories to raise 50g up 1oC and 100 x 50 x 1.00 = 5000 cal to raise the water to its boiling point.

4. Boiling water

How much heat would be required to boil the 50g of water?

The latent heat for boiling water is 540 cal/g. That means that 1g of water requires 540 cal of heat to boil.

Thus, 50g requires 50 x 540 = 27000 cal to boil.

5. Heating steam

How much heat is required to heat 50g of steam from 100oC to 110oC?

Since the specific heat of steam is 0.48 cal/g-oC, that means that 0.48 calories are needed to raise 1g up 1oC. Thus, it would take 50 x 0.48 calories to raise 50g of steam 1oC and 10 x 50 x 0.48 = 240 cal to raise the temperature of the steam to 110oC.

6. Total

The total heat required to change 50g of ice at -10oC to steam at 110oC is:

250 + 4000 + 5000 + 27000 + 240 = 36490 cal.

Summary

Heating materials like ice, water and steam increases their temperature. The specific heat of the material determines the calories required to heat one unit of mass one degree.

Changing the state of the material requires extra heat energy that is not used to change the temperature. The amount of heat required to change the state of the material is called its latent heat. The complex problem of determining how much heat is required to change ice into water and then change the water into steam should be broken into parts and solved individually.

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