Why does isentropic compression increase temperature in the Otto cycle?

[kamranonline]

I have a general question about otto cycle. If we heat a gas with constant volume its temperature rise according to PV=mRT. However during Isentropic compression(delta Q and delta S is zero), the volume is becoming less and pressure is increasing but i don't know why the temperature should increase during this process. According to the above equation the temperature can increase or decrease but i don't know why it always increases..

 

[ehild]

The internal energy of an ideal gas is proportional to its temperature. The change of internal energy in a process is

$$\Delta U = Q + W$$

where Q is the heat gained from the surroundings and W is the work of the external forces.
When Q =0, a positive external work (compression) will increase the internal energy, so the temperature will increase, too.

ehild

 

[kamranonline]

Thanks a lot... failed to think from internal energy's perspective.