The latent heat of vaporization of water is about 2.44 ×10^6 J / kg and the vapor density is 0.

step 1 In this question we have given that a gas is compressed adiabatically so that its final density

The latent heat of vaporization of water is about 2.44 ×10^6...

The latent heat of vaporization of water is about $2.44 \times 10^6 \mathrm{~J} / \mathrm{kg}$ and the vapor density is $0.598 \mathrm{~kg} / \mathrm{m}^3$ at $100^{\circ} \mathrm{C}$. Find the rate of change of the boiling temperature with altitude near sea level in ${ }^{\circ} \mathrm{C}$ per km . Assume the temperature of the air is 300 K . (Density of air at $0^{\circ} \mathrm{C}$ and 1 atm is $1.29 \mathrm{~kg} / \mathrm{m}^3$ ).

The latent heat of vaporization of water is about $2.44 \times 10^6 \mathrm{~J} / \mathrm{kg}$ and the vapor density is $0.598 \mathrm{~kg} / \mathrm{m}^3$ at $100^{\circ} \mathrm{C}$. Find the rate of change of the boiling temperature with altitude near sea level in ${ }^{\circ} \mathrm{C}$ per km . Assume the temperature of the air is 300 K .
(Density of air at $0^{\circ} \mathrm{C}$ and 1 atm is $1.29 \mathrm{~kg} / \mathrm{m}^3$ ).

Key Concepts

Clausius-Clapeyron Equation

The Clausius?Clapeyron equation relates the change in pressure to the change in temperature during a phase change. It is fundamental in predicting how the boiling point of a liquid shifts with changes in pressure, such as the decrease in boiling temperature at higher altitudes due to lower atmospheric pressure.

Latent Heat of Vaporization

Latent heat of vaporization is the energy required to convert a unit mass of a liquid into vapor at constant temperature. This concept is crucial in understanding the energy balance during phase changes and directly influences the calculation of temperature shifts under varying pressures.

Atmospheric Pressure Variation with Altitude

Atmospheric pressure decreases with altitude because the amount of overlying air decreases. This pressure variation affects the boiling point of liquids since a lower external pressure reduces the temperature required to achieve boiling, making it a key concept in determining how boiling temperatures adjust with altitude.

Ideal Gas Law

The ideal gas law, which relates pressure, volume, and temperature, provides a framework for understanding how gas properties such as density and pressure change with altitude. It is used to estimate the behavior of the atmosphere and plays an essential role in calculating pressure changes that affect boiling points.

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