It depends upon the amperage draw of the appliance. If this isn't stated, look for a wattage rating. Watts equal volts x amps. A light duty cord will heat up from a high amperage draw and cause a fire! Do NOT use appliances on that cord. They make special heavy duty appliance cords but you still have to run the calculations. You also need to know what amperage rating the breaker/ fuse has for that circuit. That means tracing the circuit back to the distribution panel. You could also have improper wiring so again, you really need an electrician in there. Talk to the landlord. If he balks, talk to the Fire Marshal. He'll force them to get it fixed.
Current codes call for two 20 ampere ground fault protected appliance circuits in the kitchen separate from the refrig., lighting and other appliances. See what you can do about getting an electrician in there before someone dies in a fire.