That depends on how you want to look at it. If you are considering that you need to run your refridgerator 24hrs a day every day to keep your food fresh, but may only need to do one or two loads of laundry a week, the refridgerator would be the more costly appliance in terms of energy.
A typical refridgerator consumes about 725 watts, while a washer takes between 350-500 watts and a dryer can consume between 1800-5000 watts.
To run your fridge for a week it would take
725watts x 24hrs x 7days = 121.8 kWh (kilowatt hours)
say you have the most inefficient washer and dryer set and do two loads a week.
washer = 500 watts x .6h X 2 = 600Watt hours
dryer = 5000 watts x 1h x2 = 10kWh
Total = 10.6kWh
Therefore your fridge will consume approximately 111.2kWh more than two loads of laundry a week.
For more information on household appliance energy use see this website.
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