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As for factors that affect the rate of the Diels Alder reaction, having an s-cis conformation is primary.

But in a case as shown below, what makes the second diene react faster compared to the third?

The only reason I can think of is that the second diene has substituents pointing outward so they cause less steric hindrance as it reacts with a dienophile thus has a lower activation barrier. Are there any other underlying reasons apart from hindrance? enter image description here

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You are correct that the having the diene in an s-cis conformation is extremely important. Only from this conformation can the Diels-Alder occur. If there is a high concentration of the s-cis conformer the Diels-Alder will likely occur rapidly; if there is a low concentration the reaction will occur more slowly.

In cyclopentadiene, the diene component has no choice, it is locked in an s-cis conformation by the ring. However with acyclic 1,3-dienes an equilibrium exists between the s-cis and s-trans conformations.

In 1,3-butadiene the amount of the s-cis conformation is relatively small (~2%) because of the steric interaction between the "internal" hydrogens at the ends of the chain in this conformation. In accord with this expectation, 1,3-butadiene is not as reactive as cyclopentadiene in the Diels-Alder reaction.

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If we replace one of these "internal" hydrogens with a methyl group (penta-1,cis-3-diene), the steric interaction between the "internal" methyl and hydrogen in the s-cis conformation is even greater, further destabilizing the s-cis conformation and reducing the amount present at equilibrium. On the other hand, replacing one of the "exterior" hydrogens with a methyl group (penta-1,trans-3-diene) doesn't cause any increased steric interference in the s-cis conformation and the amount of the s-cis conformer is about the same as 1,3-butadiene. Again, in accord with expectations, penta-1,trans-3-diene reacts at a rate similar to 1,3-butadiene, whereas penta-1,cis-3-diene reacts slower.

enter image description here

(image source)

Using this information we can make predictions for your compounds. We would expect cyclopentadiene to react the fastest because it is held in an s-cis conformation. In the case of cis, cis-2,4-hexadiene we now have an internal methyl-methyl interaction, which severely destabilizes the s-cis conformation, so there is very little present at equilibrium and this compound reacts the slowest in the Diels-Alder reaction. trans, trans-2,4-hexadiene only has an "internal" hydrogen-hydrogen interaction when in the s-cis conformation, therefore it should react about as fast as 1,3-butadiene - in between the extreme rates of the other two compounds.

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It is indeed steric hindrance. It looks a lot less severe in the picture than it actually is. Remember that each end of the line is not just a carbon atom but a methyl group $\ce{CH3}$. That means that there are three further undrawn atoms bonded to the final atom of each side of the chain.

Now making the simplistic assumption that $\ce{C-H}$ bonds are similar in length to $\ce{C-C}$ bonds and just boldly drawing the hydrogens in a $120^\circ$ angle from those final carbons we notice that one hydrogen each would land on the carbon of the opposite end of the chain — very bad. If we twisted and turned a little, we could get around that, but all of the hydrogens would still be outstandingly close to each other. Therefore, (Z,Z)-hexa-2,4-diene will have a really hard time adopting the s-cis configuration.

The middle molecule, (E,E)-hexa-2,4-diene only has two hydrogens in the middle, which would hardly even notice each other.

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