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Chapter 18: Problem 14

In what sense can a gas of diatomic molecules be considered an ideal gas, given that its molecules aren't point particles?

Short Answer

Expert verified
A diatomic gas can be considered an ideal gas under conditions of high temperature and low pressure, where the effects of molecular volume and intermolecular forces become negligible, making it behave essentially as a gas of point particles.

Step by step solution

01

Understanding Ideal Gas Approximation

An ideal gas is defined as a gas in which the particles occupy no volume and there are no attractions or repulsions between particles. Ideal gases also closely follow the ideal gas equation of state, \( PV=nRT \), where P is pressure, V is volume, n is number of molecules, R is the gas constant and T is temperature.
02

Recognizing Deviations from Ideal Behaviour

In real gases, molecules do have volume and there are interactions between molecules, leading to deviations from the ideal gas behaviour.
03

Understand Diatomic Molecule Approximation as an Ideal Gas

A diatomic gas can be considered as an ideal gas under certain conditions. These include high temperature and low pressure. At high temperature,the kinetic energy of the gas particles is so high in comparison to their potential energy due to intermolecular attractions that the effect of these forces becomes negligible. At low pressure, the volume of gas is quite high, and hence the volume of the molecules relative to the volume of the gas becomes negligible. In such conditions, the gas behaves like an ideal gas, with molecules 'acting' as point particles.

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Most popular questions from this chapter

By what factor must the volume of a gas with \(\gamma=1.4\) be changed in an adiabatic process if the kelvin temperature is to double?

One scheme for reducing greenhouse-gas emissions from coalfired power plants calls for capturing carbon dioxide and pumping it into the deep ocean, where the pressure is at least 350 atm. You're called to assess the energy cost of such a scheme for a power plant that produces electrical energy at the rate of 1.0 GW while at the same time emitting \(\mathrm{CO}_{2}\) at the rate of 1100 tonnes/hour. If \(\mathrm{CO}_{2}\) is extracted from the plant's smokestack at \(320 \mathrm{K}\) and 1 atm pressure and then compressed adiabatically to 350 atm, what fraction of the plant's power output would be needed for the compression? Take \(\gamma=1.3\) for \(\mathrm{CO}_{2} .\) (Your answer is a rough estimate because \(\mathrm{CO}_{2}\) doesn't behave like an ideal gas at very high pressures; also, it doesn't include the energy cost of separating the \(\mathrm{CO}_{2}\) from other stack gases or of transporting it to the compression site.)

Monatomic argon gas is initially at a chilly \(28 \mathrm{K}\). By what factor would you have to increase its pressure, adiabatically, to bring it to room temperature \((293 \mathrm{K}) ?\)

A \(25-\) L sample of ideal gas with \(\gamma=1.67\) is at \(250 \mathrm{K}\) and \(50 \mathrm{kPa}\). The gas is compressed isothermally to one-third of its original volume, then heated at constant volume until its state lies on the adiabatic curve that passes through its original state, and then allowed to expand adiabatically to that original state. Find the net work involved. Is net work done on or by the gas?

External forces compress 21 mol of ideal monatomic gas. During the process, the gas transfers 15 kJ of heat to its surroundings, yet its temperature rises by \(160 \mathrm{K}\). How much work was done on the gas?
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