how does gear efficiency ratios work if there is the 1st law of thermodynamics? By gear efficiency ratios i mena http://www.howstuffworks.com/gears.htm

None of the laws of Thermodynamics refer directly to efficiency.

 

Mechanical systems (machines) Efficiency is output work divided by input work.

 

This also equals the mechanical advantage divided by the velocity ratio.

 

http://www.slideshare.net/jbishopgcms/mechanical-advantage-and-efficiency

 

and

 

http://www.learneasy.info/MDME/MEMmods/MEM23041A/dynamics/simple_machines/simple_machines.html

Since you mention the first law of thermo, is this a question about mechanical advantage? The HSW page is not clear on anything that might violate that law.

 

In general, mechanical advantages are about power and force, not the work done. You exert the force over a longer path, so the work is the same (there's the compliance with the first law) but gearing allows you to exert a smaller force and since it takes longer, there is a smaller power requirement, but Pt is still the same. (You can also reverse this effect, if you want.)