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Chapter 3: Problem 1

A real gas closely approaches the behaviour of an ideal gas at (a) 15 atmospheres and \(220 \mathrm{~K}\) (b) 1 atm and \(273 \mathrm{~K}\) (c) \(0-5 \mathrm{~atm}\) and \(500 \mathrm{~K}\) (d) 15 atm and \(500 \mathrm{~K}\)

Short Answer

Expert verified
The condition in which a real gas behaves most closely to an ideal gas is when the pressure is \(0 - 5 \mathrm{~atm}\) and the temperature is \(500 \mathrm{~K}\).

Step by step solution

01

Analyze the given conditions

The conditions given are different combinations of temperature and pressure. Our task is to identify the combination where a real gas behaves most closely to an ideal gas. According to the Kinetic Theory of Gases, real gases behave most like ideal gases at high temperatures and low pressures.
02

Apply the Theory

Out of the given options, let's map the theory on each combination: (a) 15 atmospheres and \(220 \mathrm{~K}\): High pressure and low temperature, so the gas is likely to behave less ideally. (b) 1 atm and \(273 \mathrm{~K}\): Low pressure and relatively higher temperature, so the gas is likely to behave more ideally. (c) \(0-5 \mathrm{~atm}\) and \(500 \mathrm{~K}\): Very low pressure and high temperature, so the real gas is most likely to behave like an ideal gas in this condition. (d) 15 atm and \(500 \mathrm{~K}\): High pressure and high temperature, so the gas is likely to behave less ideally due to high pressure.
03

Conclude the result

Using the principle that gases tend to behave as ideal gases under high temperature and low pressure conditions, we can conclude that option (c) \(0-5 \mathrm{~atm}\) and \(500 \mathrm{~K}\) would be the condition in which a real gas would most closely mimic the behaviour of an ideal gas.

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Most popular questions from this chapter

An ideal gas, obeying kinetic theory of gases, can be liquefied: (a) It cannot be liquefied at any \(P\) and \(T\) (b) Its pressure is more than \(P\) at a temperature less than \(T\) (c) Its temperature is more than critical temperature \(T\) (d) Its pressure is more than critical pressure \(P\)

An ideal gas cannot be liquefied because (a) its critical temperature is always above \(0^{\circ} \mathrm{C}\) (b) its molecules are relatively smaller or in size (c) it solidifies before becoming a liquid (d) forces operative between its molecules are negligible

According to the van der Waals correction to get the pressure of ideal gas in observed pressure a definite fraction for correction is (a) subtracted (b) added (c) divided (d) unchanged

The gas that is heated up during Joule-Thomson effect at ordinary temperature is: (a) \(\mathrm{O}_{2}\) (b) \(\mathrm{CO}_{2}\) (c) \(\mathrm{H}_{2}\) (d) \(\mathrm{SO}_{2}\)

Degrees of freedom in a water molecule are (a) 1 (b) 2 (c) 3 (d) 4
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