During Shabbat, we unscrew the light bulb in our refrigerator so that it won’t light up when we open the door. However, often on Shabbat as any other day, someone opened the refrigerator door and the refrigerator engine started up to cool the air. Is this a problem?

According to Rabbi Shlomo Zalman Orbach zatza"l. It is permitted to open the refrgerator because 1. starting the motor is a rabbinic prohibition and not from the Torah (as opposed to turning on a filament light bulb which is a Torah prohibition) 2. You don't know for sure you will turn it on at this time. Many Rabbis disagree with the first premise. Some suggest only opening the refrigerator after the motor goes on, and some people put it on a timer so there is a period when it cannot go on. All the opinions have valid Torah sources and you should consult your own Rabbi as to your personal approach.