Relative stability of cis and trans cycloalkenes

Why is the stability of (*Z*)-cyclodecene **2** greater than that of (*E*)-cyclodecene **1**?


[![enter image description here](https://i.stack.imgur.com/SKGvW.png)](https://i.stack.imgur.com/SKGvW.png)


I'd think that since **1** contains a *trans* double bond instead of a *cis* double bond, it should experience less steric repulsion and hence be more stable.


However, I've read that the *cis* isomer **2** is more stable than the *trans* isomer **1** if the ring size is 11 or smaller. For ring sizes larger than 11, the opposite is true.


Why is this so? Also, what would happen if there were more double bonds?




Usually *trans*-olefins are more stable than their *cis* isomers for steric reasons, like you suggested. However in small and medium size rings this is not the case; here the *cis*-cycloalkene is more stable than the corresponding *trans* isomer.


*trans*-Cyclooctene is the smallest trans-cycloalkene that is stable at room temperature (*trans*-cyclohexene and *trans*-cycloheptene have been detected as short-lived intermediates). In your drawing up above of *trans*-cyclodecene (a) draw in the two hydrogens on the *trans* double bond. One of them is "inside" the ring and causes steric problems with the carbons on the other side of the ring as pictured below. Because of this destabilizing transannular interaction *trans*-cycloalkenes with up to around 11 carbons do not exist as planar molecules. They exist in a conformation as pictured below for *trans*-cyclooctene.


![enter image description here](https://i.stack.imgur.com/fDQsu.png) 


([image source](http://www.organicchemistry.com/cycloalkenes-and-cycloalkynes/))


If you can, build a model of *trans*-cyclooctene. Notice how you have to pull and stretch the methylene chain in order to attach that last methylene back onto the other end of the double bond - there is a lot of strain in this molecule. Now build a model of *cis*-cyclooctene; it is easy to loop the methylene chain from one end of the double bond to the other end. 


Not until you get to around *trans*-cyclododecene (12 carbons) do you have enough carbons to easily connect from one end of the *trans* double bond back to the other end. ***trans*-Cycloalkenes with less than 12 carbons have additional strain because of this difficulty in spanning the double bond**. Once you get to around 12 carbons there is no difficulty spanning the double bond and so once again *trans*-cycloalkenes become more stable than their *cis* counterparts.


Since double bond carbons are $\mathrm{sp^2}$ hybridized with 120° angles, if we add more double bonds, the 120° angles make it more difficult to loop the more flexible $\mathrm{sp^3}$ methylene (with their 109.5° angles) chain around the double bonds.


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