Latent Heat and conservation of energy

• rico22
In summary, the problem involves a cooking vessel with 11.0 kg of water and an unknown mass of ice at 0°C. The temperature remains constant at 0°C for the first 50.0 min and then increases to 2.00°C from 50.0 min to 60.0 min. By using the equations Q=mcΔT, Q= mL, and Qhot + Qcold=0, and making the assumption that the heater element delivers constant power, the initial mass of ice can be determined to be 0.269 kg.
rico22

Homework Statement

A cooking vessel on a slow burner contains 11.0 kg of water and an unknown mass of ice in equilibrium at 0°C at time t = 0. The temperature of the mixture is measured at various times. During the first 50.0 min, the mixture remains at 0°C. From 50.0 min to 60.0 min, the temperature increases to 2.00°C. Ignoring the heat capacity of the vessel, determine the initial mass of ice.

Q =mcΔT; Q= mL

cwater=4186
Lfusion=333000

Qhot + Qcold=0

The Attempt at a Solution

miceLfusin+micecwaterΔT+mwatercwaterΔT = 0

mice(333000) + mice(8372) + 92092 = 0

This gives me mice = 0.269kg but i know this is wrong. Any pointers would be greatly appreciated.

During the melting phase all the energy goes into melting the ice (water stays at zero) so

Mice * Lfusion = Power * Timemelt

After melting during the heating phase..

(Mwater + Mice) * Cwater * ΔT = power * Timeheat

Two unknowns and two equations.

Thanks for the reply... I reworked the problem but I am still getting it wrong somehow...

ok now I got it... I mustve been doing something wrong with the calculations...how did you know to bring power into the formula?

What is the definition of power?

rico22 said:
...how did you know to bring power into the formula?

I started by writing out..

Mice * Lfusion = Emelt

but then you get stuck because there isn't enough info in the problem statement to calculate the energy and the timing information hadn't been used.

Energy is related to power using...

Power = Energy/time

or

Energy = Power * Time.

I made the reasonable assumption that the heater element delivered constant power.

ok thank you!

1. What is Latent Heat?

Latent heat is the amount of heat energy that is required to change the phase of a substance (solid, liquid, or gas) without changing its temperature. It is the energy that is needed to break or form the intermolecular bonds between particles in a substance.

2. How does Latent Heat relate to the conservation of energy?

Latent heat is an example of the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. When a substance undergoes a phase change, the energy is either absorbed or released in the form of latent heat, while the total energy in the system remains constant.

3. What are some examples of Latent Heat?

Some common examples of latent heat include the energy absorbed when ice melts into water, or when liquid water evaporates into water vapor. On the other hand, energy is released when water vapor condenses into liquid water, or when liquid water freezes into ice.

4. How does Latent Heat affect the Earth's climate?

Latent heat plays a crucial role in regulating the Earth's climate. The energy absorbed during evaporation from the Earth's surface is released into the atmosphere when water vapor condenses into clouds, which helps to moderate temperature changes. Additionally, latent heat released by tropical ocean waters fuels the formation of hurricanes and typhoons.

5. Can Latent Heat be harnessed as a source of energy?

Yes, latent heat can be harnessed as a source of energy in a process called phase change energy storage. This involves using the energy absorbed or released during phase changes to heat or cool buildings or to power engines. For example, ice can be used to store thermal energy during the melting process and then released during the freezing process to provide heating for a building.

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