[chermi]

Yes, you can explain refrigeration with ideal gas. But...

You need non-ideal gas (attraction) to get temperature inversion. Then you just need compressor and voila, look at PT charts to find what temperature range you need. With ideal gas reverse carnot refrigerator your refrigeration effect is bounded on low temperature side by the available low temperature source.

So yes, you can refrigerate with ideal gas, but it's not very helpful in warm areas or if you need to get something super cold.