How many kilocalories kcal of heat are needed when 70 g of water is converted to steam at 100 oc

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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.)

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.

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.

Heat up your thinking

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Our water heating calculator can help you determine both the amount of heat required to raise the temperature of some H2O and the time it will take. It considers the heat capacities of all three states of matter, so it also works if you want to melt the ice or boil water.

If you're wondering what's the limit of how hot water can get, what is the heat capacity, and how it all relates to your water heater BTU (British Thermal Unit) - read on!

This question may sound trivial, but is it really? Yes and no. Although it seems obvious to think of a kettle, stove, boiler, or another device, all of them are just tools that we use to change the temperature more easily.

To heat water, you need to... well, add heat, which is one of the forms of energy. Doing so increases the average kinetic energy of the molecules and hence also the directly proportional temperature, as stated in the kinetic theory. There are three types of heat transfer:

• Conduction occurs when two objects are in contact. There's a certain heat flow from the hot object to the cooler via molecule agitation (collision of high-speed particles with the slower ones). Some substances are better conductors than others, so we're usually interested in material's thermal conductivity. An example of this type of transfer would be a pan on the stove or holding an ice cube in your hand.
• Convection applies to fluids (including air!). When the liquid's temperature increases, it becomes less dense and rises. At the same time, the cooler counterparts will move downwards, creating convection currents. They are circular movements that help spread the heat throughout the substance. It explains, for example, why the ocean water is warmer on the surface than if you swim deeper.
• Radiation, on the contrary, doesn't need molecules as it happens via electromagnetic waves. It means that no medium nor physical contact is required. All objects emit and absorb radiation, some more than others. Stefan-Boltzmann Law tells us how much power is radiated from a body at a certain temperature. This is how Earth gets the heat from the Sun.

All of these methods of heat transfer apply to our case, but it's unlikely that you're going to consider radiation for everyday purposes. Nevertheless, the method doesn't impact the amount of heat required to raise the temperature, so our water heating calculator will help you even in a more unusual setting.

Talking about heat may be confusing. There are a few terms that sound similar but mean completely different things. However, they're all critical to understanding how to calculate the energy needed to heat water, so we've gathered all of them with an explanation:

• Heat, as we've mentioned, is one of the forms of energy that's transferred because of temperature difference. Therefore its units are, typically, Joules (J).
• Specific heat capacity is a property of the material defined as the amount of heat required to raise the temperature of 1 kilogram of a substance by 1 Kelvin (or Celcius, since the scale is the same in terms of increments - an increase of 1 K is equal to an increase of 1 °C ). It follows that its units are J/kgK or J/(kg°C). The British thermal unit (BTU) is defined similarly but talks about raising the temperature of a pound of H2O by 1 degree Fahrenheit. Hopefully, you see how the water heater BTU is related to this now!
• Latent heat, on the contrary, doesn't refer to a change in temperature but a phase. This is the amount of heat required to turn, e.g., a liquid of some mass into a gas - you could think of what happens to water at 100°C when it becomes steam. In this case, the units are J/kg.

Although sporadically considered, it's worth knowing that the value of latent heat changes with the pressure, whereas the specific heat varies depending on the temperature. The water heating calculator uses the most standard values of these constants.

The amount of energy you'll need to change the temperature of the water depends on its initial and final states. Generally, you need to consider two quantities:

• Heat required to raise the temperature, Qt:

Qt = c * m * (Tf - Ti),

where:

• c is the specific heat capacity;
• m is the mass (you can find it knowing the volume, too!);
• Tf is the final temperature; and
• Ti is the initial temperature.

• Heat needed to change the phase, Qp:

Qp = L * m,

where:

• L is the latent heat. If there's a transition from ice to water, we're considering the latent heat of fusion, whereas for the phase change from liquid into steam, it's the latent heat of vaporization.

Finally, all you need to do is sum up all heat values to calculate the energy needed to heat H2O. For just one phase, you'll have a single number, but otherwise, there's going to be more. Luckily, our water heating calculator takes care of it for you!

If you know the efficiency and the power of the heater, you can also compute the time required to reach the final temperature. The formula is:

time = Qtotal / (efficiency * power),

where:

• Qtotal is the total energy found earlier.

How much energy would you need to obtain water hot enough to brew some tea from a 1 kg block of ice with an initial temperature of -10°C (263.15 K)? We can break it into smaller steps:

1. Calculate the heat needed to raise the temperature of ice until 0°C:

Qice = 1 kg * 10 K * 2108 J/(kg * K) = 21 080 J.

1. Find the amount of heat required to convert it into water:

Qice->water = 1 kg * 334 000 J/kg = 334 000 J.

1. Determine how much energy you need to heat the water. Let's assume that the perfect temperature would be 96°C (369.15 K):

Qwater = 1 kg * 96 K * 4190 J/(kg * K)= 402 240
J.

1. Sum up all the values to get the total energy needed:

Qtotal = 21 080 + 334 000 + 402 240 = 757 320 J.

1. An average kettle has 1800 Watts (W) of power. Assuming 90% efficiency, we can see that:

time = 757 320 J / (90% * 1800 W) = 467.48 s ≈ 7 minutes.

As you've probably noticed, this calculation may be a bit laborious and take almost as long as melting a block of ice. Perhaps it's a better idea to use the water heating calculator and get to work right away then!

The specific heat of water is 4190 J/(kg*°C). It means that it takes 4190 Joules to heat 1 kg of water by 1°C.

Yes, water has a high heat capacity due to the hydrogen bonding amongst the molecules. When the temperature increases, the particles move more freely. For this to happen, the hydrogen bonds need to be broken, which requires a lot of energy (heat) to be absorbed.

The latent heat of fusion of water is 334,000 J/kg. Therefore, 334 J of energy are required to melt 1 g of ice at 0°C.

Water's latent heat of vaporization is 2,264,705 J/kg. This is the amount of heat you need to turn 1 kg of a liquid into a vapor, without a rise in the temperature of the water.

The heat capacity of ice is 2108 J/(kg*°C). Therefore, you'd need to input 2108 Joules to heat 1 kilogram of ice by 1°C.

Steam is the state of water with the lowest specific heat of 1996 J/(kg*°C). It means that heating 1 kg of steam by 1°C requires 1996 Joules of heat.