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Ideal Gas Law

The ideal gas law is an equation of state of a hypothetical ideal gas. It is an approximation to the behaviour of many gases under many conditions. The ideal gas law however has many limitations. Emile Clapeyron was the first the state the equation in 1834 as a combination of Boyle’s law and Charles’ law. The ideal gas law is

PV = nRT

Where P is pressure, V is volume, n is the number of moles, T is the temperature, and R is the universal gas constant.

In Statistical mechanics, the ideal gas law is

PV = NkT

Where P is the absolute pressure, V is the volume, N is the number of particles in the gas, k is the Boltzmann constant and T is the temperature.

These equations only apply to ideal gas. There are many other forms of equations of states. The ideal gas law neglects both molecular size and intermolecular attractions. It is most accurate for monatomic gases at high temperatures and low pressures. The neglect of molecular size becomes less important for lower densities. 

When, where, and why would anybody pay any attention to Bernoulli's Law?

Bernoulli's equation only yields perfect predictions if the following conditions exist: 1. The liquid is inviscid; that is, it has no viscosity, and offers no frictional resistance to movement through it. (In other words, not like honey. More like alcohol, although even alcohol has some viscosity.) 2. Steady flow; that is, n

Molar volume of gas, from perfect gas law and from van der Waals equation

Calculate the molar volume of chlorine gas at 350 K and 2.30 atm using (a) the perfect gas law and (b) the van der Waals equation. Use the answer to (a) to calculate a first approximation to the correction term for attraction, and then use successive approximations to obtain a numerical answer for part (b).

Gas in two containers connected by a small hole

A container is divided into 2 parts by a partition containing a hole of radius r. Helium gas in the two parts is held at temperature T1 = 75K and T2 = 300K respectively. After the system reaches a steady state, the mean free paths on each side are lambda1 and lambda2. What is the ratio lambda1/lambda2 when (a) r>>lambda1 and

The Temperature of an Ideal Gas

The temperature of an ideal gas at an initial pressure P1 and volume V1 is increased at constant volume until the pressure is doubled. The gas is then expanded isothermally until the pressure drops to is original value, where it is compressed at constant pressure until the volume returns to its initial value. (a) sketch these pr

Pressure for Welding

A welder using a tank of volume 7.50×10^(−2) m^3 fills it with oxygen (with a molar mass of 32.0 g/mol) at a gauge pressure of 2.80×105 Pa and temperature of 38.0C. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is 22.4C, the gauge pressure of the oxygen in the tank is

Ideal gas problem.

A certain gas cylinder A has a volume of 4.78 L and contains O2(g) at 927 mm Hg and a temperature of 25°C. A second gas cylinder B, with an unknown volume, contains Ne(g) at 25°C and a pressure of 898 mmHg. When the two cylinders are connected and the two gases are allowed to completely mix, the pressure in each cylinder becom

Differential Equation with the Clausius-Clapeyron Relation

dP/dT = L/T deltaV, is a differential equation that can, in principle, be solved to find the shape of the entire phase-boundary curve. To solve it, however, you have to know how both L and deltaV depend on temperature and pressure. Often, over a reasonably small section of the curve, you can take L to be constant. Moreover, i

Does Venus Have a Thicker Atmosphere Than Earth?

On the sunlit surface of Venus, the atmospheric pressure is 9.0 x 10 6Pa, and the temperature is 740K. On the earth's surface the atmospheric pressure is 1.0 x 10 5Pa, while the surface temp can reach 320K. These data imply that Venus has a "thicker" atmosphere at its surface than does the earth, which means that the number of m

Nitrogen balloon: volume, number of moles, and mass of nitrogen in the balloon

A round balloon had a radius of 0.30 m & contains nitrogen (N2) at 30 degrees Celsius and one atmosphere total pressure. a) What is the volume of the nitrogen in the balloon? b) How many moles of nitrogen are in the balloon? c) What is the mass of the nitrogen in the balloon? d) If the balloon is then submerged in a body o

Solving Ideal Gas Law Problems

Please help with the following problem. Provide step by step calculations. A round balloon had a radius of 0.30 m & contains nitrogen (N2) at 30 degrees Celsius and one atmosphere total pressure. What is the volume of the nitrogen in the balloon? How many moles of nitrogen are in the balloon? What is the mass of the nitrogen

An ideal gas at STP (1 atm and 0°C) is taken through a process where the volume is expanded from 25 L to 50 L. During this process the pressure varies inversely as the volume squared, so that P = 0.2 alpha/V^2

An ideal gas at STP (1 atm and 0°C) is taken through a process where the volume is expanded from 25 L to 50 L. During this process the pressure varies inversely as the volume squared, so that P = 0.2 alpha/V^2 (a) Determine the constant alpha in standard SI units. (b) Calculate the number of moles of gas present. (c) F

Archimedes Principle and Buoyancy

Hi. Can someone please walk me through the following problem? A 0.12 kg balloon is filled with helium (density = 0.179 kg/m^3). If the balloon is a sphere with a radius of 5.2 m, what is the maximum weight it can lift? Thank you!

Multiple choice questions on Heat

A house has well-insulated walls. It contains a volume of 100 m^3 of air at 300 K. Calculate the energy required to increase the temperature of this diatomic gas by 2 degree C. Assume it is heating of constant pressure and use Cp = 7R/2. ================================================= Answers: a) 118 kJ b) 236 kJ c) 354

The Ideal Gas Law

At the start of a trip, a driver adjusts the absolute pressure in her tires to be 2.82*10^5 Pa when the outdoor temperature is 286 K. At the end of the trip she measures the pressure to be 2.98*10^5 Pa. Ignoring the expansion of the tires, find the air temperature inside the tires at the end of the trip.

Macroscopic Description of an Ideal Gas

A rigid tank contains 0.40 mol of oxygen (02). Determine the mass (in kg) of oxygen that must be withdrawn from the tank to lower the pressure of the gas from 40 atm to 25 atm. Assume that the volume of the tank and the temperature of the oxygen are constant during this operation. Thanks