# Ideal gas law problem concerning the exponetial atmosphere: part 4

• pentazoid
In summary, The ideal gas law is a fundamental equation in thermodynamics that describes the behavior of an ideal gas. It states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT. This law is often used to model the behavior of gases in the Earth's atmosphere, including the exponential decrease in pressure with increasing altitude. To calculate the pressure at a specific altitude in the exponential atmosphere, the ideal gas law can be used in its rearranged form P = nRT/V. However, it is not perfectly applicable to real gases in the Earth's atmosphere, and other equations of state may be needed for more accurate calculations. The ideal gas law also explains the relationship between temperature and pressure in the exponential atmosphere through
pentazoid
1. Homework Statement [/b
Estimate the pressure , in atmospheres, at the following locations:Odgen Utah(1430 m above seas level);Leadville colorado(3090 m) Mt. Whithney (4420 m) and various other cities above sea level. (assume that the pressure at sea level is 1 atm.)

## Homework Equations

P(z)=P(0)exp(-mgz/kT)?

## The Attempt at a Solution

P(0)=1.0105e5 pascal = 1 atm.
how would I determine the mass and temperature. should I consider the molar mass of air molecules?

anybody not understand my question or/and my solution

## 1. What is the ideal gas law and how does it relate to the exponential atmosphere?

The ideal gas law is a fundamental equation in thermodynamics that describes the behavior of an ideal gas. It states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature. The ideal gas law is often used to model the behavior of gases in the Earth's atmosphere, including the exponential decrease in pressure with increasing altitude.

## 2. How is the ideal gas law used to calculate the pressure at a specific altitude in the exponential atmosphere?

To calculate the pressure at a specific altitude in the exponential atmosphere, we can use the ideal gas law in its rearranged form P = nRT/V. We first calculate the number of moles of gas present at the given altitude, using the ideal gas law and the known pressure, volume, and temperature at sea level. We then plug this value into the rearranged equation along with the given temperature at the specific altitude, and solve for P to obtain the pressure at that altitude.

## 3. Is the ideal gas law applicable to real gases in the Earth's atmosphere?

The ideal gas law is not perfectly applicable to real gases in the Earth's atmosphere, as real gases do not always follow the ideal gas behavior. However, it is a good approximation for most gases at moderate pressures and temperatures. For more accurate calculations, other equations of state, such as the van der Waals equation, can be used.

## 4. How does the ideal gas law explain the relationship between temperature and pressure in the exponential atmosphere?

The ideal gas law explains the relationship between temperature and pressure in the exponential atmosphere through the direct relationship between temperature and the average kinetic energy of gas molecules. As temperature increases, the average kinetic energy of gas molecules also increases, causing them to collide with the walls of their container (in this case, the Earth's atmosphere) with more force, resulting in a higher pressure.

## 5. Can the ideal gas law be used to predict the behavior of gases in non-exponential atmospheres?

The ideal gas law is most accurate in predicting the behavior of gases in exponential atmospheres, where pressure decreases exponentially with increasing altitude. In non-exponential atmospheres, the ideal gas law may still provide a good approximation, but more complex equations or models may be needed to accurately predict the behavior of gases. Additionally, the ideal gas law assumes that gas molecules are point masses with no volume, which is not always the case in real gases.

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