Liquid helium- 4 has a normal boiling point of 4.2 K ....

Name: Problem 139, Chapter 1: Problems and Solutions on Thermodynamics and Statistical Mechanics
Uploaded: 2020-09-17T12:50:57-08:00
Duration: 56 s
Channel: Sheh Lit Chang
Description: Liquid helium- 4 has a normal boiling point of 4.2 K . However, at a pressure of 1 mm of mercury, it boils at 1.2 K . Estimate the average latent heat of vaporization of helium in this temperature range.

Liquid helium- 4 has a normal boiling point of 4.2 K . However, at a pressure of 1 mm of mercury, it boils at 1.2 K . Estimate the average latent heat of vaporization of helium in this temperature range.

Key Concepts

Clausius-Clapeyron Equation

This equation relates the rate of change of pressure with temperature during a phase transition to the latent heat of the process. It provides a crucial link between the logarithmic derivative of the vapor pressure and the latent heat, using the relation d(ln P)/dT = L/(RT^2) under appropriate assumptions, such as ideal gas behavior for the vapor phase.

Latent Heat of Vaporization

This is the heat energy required per unit mass or per mole to convert a liquid into vapor at constant temperature and pressure. It encapsulates the energy needed to overcome intermolecular forces during the phase change from liquid to gas.

Phase Equilibrium

This concept refers to the state where two distinct phases, such as liquid and vapor, coexist in a stable balance at a given temperature and pressure. Understanding phase equilibrium is essential for analyzing boiling points and calculating latent heats, since it is at equilibrium that latent heat measurements are meaningful.

Boiling Point

The boiling point is defined as the temperature at which a liquid's vapor pressure equals the surrounding external pressure, leading to rapid vaporization. This concept is fundamental when examining phase transitions and is directly linked to the calculation of latent heat using thermodynamic relations.

Vapor Pressure Dependence on Temperature

Vapor pressure increases with temperature, and its relation with temperature is a key factor in phase transition analysis. This dependence is used in the Clausius-Clapeyron equation to connect the change in vapor pressure with the latent heat of vaporization over a temperature interval.

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