Consider a gas of neutrons. Does it obey the ideal gas equation much better than hydrogen gas at the same temperature and pressure?
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5$\begingroup$ Sounds like you have a teacher who wants you to think. $\endgroup$– user137289Commented Feb 17, 2018 at 21:49
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4$\begingroup$ And what you are expected to think about is the assumptions on which the model called "an ideal gas" is based and how well two actual, physical systems agree with those assumptions. I have to say I rather like this question because I can see at least two valid lines of inquiry that give different answers. Spotting both of them requires paying attention to the implicit assumptions as well as the explicit ones. Nice. $\endgroup$– dmckee --- ex-moderator kittenCommented Feb 17, 2018 at 22:19
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It will not be easy to establish a pure neutron gas in thermal equilibrium to test the ideal gas law.
(1) Free neutrons have a life time of only 14.7 minutes. They decay (predominantly) into a proton, an electron, and an electron antineutrino. So you will always have positive protons and electrons and thus hydrogen around.
(2) It is not easy to contain neutrons in a vessel because due to the missing electric charge they will easily escape through any walls.
The neutron-neutron scattering cross section is probably very low.
Added later: The above does not yet answer the question, as @JohnRennie has rightly pointed out. To come closer to an answer, I add the following reasoning based on the van der Waals equation which has two constants $a$ and $b$ which describe the deviation from the ideal gas law.
The answer depends on the question how the "molecular volume" and the "intermolecular force" of thermal neutrons compares to those of molecular hydrogen. These two effects are represented by the constants $a$ and $b$ in the van der Waals equation $$(p+a/V_m^2)(V_m-b)=R T$$ and they describe the deviation from the ideal gas law. Here $p$ is the pressure, $V_m$ the molar volume, $R$ the ideal gas constant, $T$ the absolute temperature. The constant $a$ is a measure of the inter-molecular force, the constant $b$ the actual volume of a mole of the gas molecules.
I would consider it a very rough estimate to assume that the constant $b$ describing the molecular volume of the neutrons should be much smaller (many orders of magnitude) than the corresponding molecular volume of hydrogen. Also, the forces between hydrogen molecules expressed by the constant $b$ are probably stronger than between neutrons. But the latter is only a wild guess. Thus a neutron gas is probably closer to an ideal gas than the hydrogen gas.
answered Feb 18, 2018 at 1:27
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$\begingroup$ Thermal neutron gasses have (more or less by definition) the same kinetic temperature as their surroundings, and as the expand by diffusion you can compute the pressure from their mean free path. Places like fixed-target accelerator end stations often generate a continuous supply and establish a thermalized cloud of neutrons in their immediate vicinity (so safety protocols for non-emergency access have a minimum time after beam-off before entry). Not that it is easy to experiment on such gasses, but they aren't just figments of the author's imagination. $\endgroup$ Commented Feb 18, 2018 at 1:34
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$\begingroup$ @dmckee - You are right. Thermal neutrons by equilibration with a scattering environment exist. I am not sure about a possible thermal equilibration by interactions between neutrons themselves. $\endgroup$ Commented Feb 18, 2018 at 1:51
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$\begingroup$ While this is all true it doesn't answer the question. $\endgroup$ Commented Feb 18, 2018 at 9:08
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$\begingroup$ @JohnRennie -I agree. The answer depends on the question how the "molecular volume" and neutron-neutron "molecular interaction force" of thermal neutrons compares to the hydrogen molecular volume and interaction force as expressed by the constants $a$ and $b$ in the van der Waals equation. The constants of hydrogen known. I expanded my answer with guesses in regard to the possible constants of neutrons. $\endgroup$ Commented Feb 18, 2018 at 14:52