/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 59 Liquid helium has a very low boi... [FREE SOLUTION] | 91Ó°ÊÓ

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Liquid helium has a very low boiling point, \(4.2 \mathrm{~K}\), as well as a very low latent heat of vaporization, \(2.00 \times 10^{4} \mathrm{~J} / \mathrm{kg}\). If energy is transferred to a container of liquid helium at the boiling point from an immersed electric heater at a rate of \(10.0 \mathrm{~W}\), how long does it take to boil away \(2.00 \mathrm{~kg}\) of the liquid?

Short Answer

Expert verified
It takes approximately 1.11 hours to boil away 2.00 kg of the liquid helium.

Step by step solution

01

Calculate the total energy needed for phase change

The total energy (\(Q\)) required for the phase change can be calculated by multiplying the latent heat (\(L\)) with the mass of the substance (\(m\)). Here \(L = 2.00 \times 10^{4} \mathrm{~J/kg}\) and \(m = 2.00 \mathrm{~kg}\). So, \(Q = m \times L = 2.00 \times 10^{4} \mathrm{~J/kg} \times 2.00 \mathrm{~kg} = 4.00 \times 10^{4} \mathrm{~J}\).
02

Calculate the time required for phase change

The time (\(t\)) required for the phase change can be calculated by dividing the total energy (\(Q\)) with the power (\(P\)) of the heater. Here \(P = 10.0 \mathrm{~W}\) and \(Q = 4.00 \times 10^{4} \mathrm{~J}\). So, \(t = Q / P = 4.00 \times 10^{4} \mathrm{~J} / 10 \mathrm{~W}\ = 4.00 \times 10^{3} \mathrm{~s}\) or approximately 1.11 hours.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Phase Change
Understanding the concept of a phase change is crucial in thermal physics. It's the transformation of a substance from one state of matter—solid, liquid, or gas—to another. Each substance has specific temperatures and pressures at which these changes occur. For instance, when a liquid becomes a gas, this is known as vaporization or boiling.During a phase change, the temperature of a substance doesn't increase despite the input of heat. This is because the energy is used to alter the substance's structure, overcoming intermolecular forces, rather than increasing its kinetic energy. The phase change of liquid helium, as seen in the exercise, demonstrates this principle with its transition from liquid to gas at a boiling point of just 4.2 K.
Boiling Point
The boiling point of a substance is the temperature at which it changes from a liquid to a gas. The boiling point varies based on the ambient pressure; for example, water boils at a lower temperature at higher altitudes where atmospheric pressure is lower.

Boiling Point and Pressure

Materials like helium have their own unique boiling points, and for liquid helium, it's extremely low at 4.2 K. This is why helium is often used in cryogenics. The low boiling point indicates that helium does not need much heat to transition into gas.
Heat Transfer
Heat transfer is the movement of thermal energy from one object or substance to another. It can occur through conduction, convection, or radiation. In the exercise, an electric heater transfers energy to the liquid helium, causing it to boil away.

Modes of Heat Transfer

  • Conduction: Transfer of heat through direct contact.
  • Convection: Transfer of heat through a fluid (liquid or gas) caused by molecular motion.
  • Radiation: Transfer of heat in the form of electromagnetic waves, without needing a medium.
These principles dictate how quickly heat can be transferred and are dependent on the temperature difference and properties of the substances involved.
Thermal Physics
Thermal physics deals with the properties of temperature, heat, and their effect on matter. The study includes understanding concepts like thermal expansion, heat transfer, phase transitions, and thermodynamics laws.In the context of the given exercise, it explains how energy from the heater is used to change the phase of helium from liquid to gas. Understanding the principles of thermal physics enables us to solve practical problems such as calculating the time needed to boil a certain amount of liquid helium using a heater with a known power output.
Specific Latent Heat
Specific latent heat is the amount of heat required to change the state of a unit mass of a substance without changing its temperature. It's usually expressed in joules per kilogram (J/kg).

Latent Heat in Phase Transitions

There are two kinds of latent heat:
  • Latent heat of fusion: Heat required for a solid to become a liquid (melting), or the heat released when a liquid becomes a solid (freezing).
  • Latent heat of vaporization: Heat needed for a liquid to become a gas (vaporization), or the heat released when a gas becomes a liquid (condensation).
In the helium example, the latent heat of vaporization is notably low, signifying that it takes a smaller amount of heat to transition from liquid to gas compared to other substances.

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Most popular questions from this chapter

\(\mid \mathbf{C}\) A \(3.00-g\) lead bullet at \(30.0^{\circ} \mathrm{C}\) is fired at a speed of \(2.40 \times 10^{2} \mathrm{~m} / \mathrm{s}\) into a large, fixed block of ice at \(0{ }^{\circ} \mathrm{C}\), in which it becomes embedded. (a) Describe the energy transformations that occur as the bullet is cooled. What is the final temperature of the bullet? (b) What quantity of ice melts?

The highest recorded waterfall in the world is found at Angel Falls in Venezuela. Its longest single waterfall has a height of \(807 \mathrm{~m}\). If water at the top of the falls is at \(15.0^{\circ} \mathrm{C}\), what is the maximum temperature of the water at the bottom of the falls? Assume all the kinetic energy of the water as it reaches the bottom goes into raising the water's temperature.

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In a showdown on the streets of Laredo, the good guy drops a \(5.00-\mathrm{g}\) silver bullet at a temperature of \(20.0^{\circ} \mathrm{C}\) into a \(100-\mathrm{cm}^{3}\) cup of water at \(90.0^{\circ} \mathrm{C}\). Simultaneously, the bad guy drops a \(5.00-\mathrm{g}\) copper bullet at the same initial temperature into an identical cup of water. Which one ends the showdown with the coolest cup of water in the West? Neglect any energy transfer into or away from the container.

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