How long would it take a 2,000 Watt electric unit heater to convert 20 kW-hr of electrical energy into heat energy when connected to a 200V source? The heater is rated 200Volts.

p=work/time

yes, that's what I did. In which I get 10 hours as the duration. But if you will notice, the voltage wasn't used. Our professor told us that the voltage is essential in answering the question. By the way, this also has a follow question: How long would it take if the electric heater unit is connected to a 100 volt source?

The voltage is not at all required for calculating time. However, the voltage is useful if you wanted to know the current consumption and resistance of heater. P = VI. Therefore, current I = 10 A P = I^2 * R. Therefore, R = 20 ohms. And as for what happens when ,voltage becomes 100V - remember that for a constant resistance, power is proportional to square of voltage. Since voltage is now half, power is one-fourth the earlier value (500W). So, the time requires increases by the same amount. i.e, now the time to consume the energy is 40 hours.

ah yeah. I forgot that. But isn't it that power is proportional to voltage. not the square of it. And if that's so, then the power is half the original value (1000W). So, the time is increased (doubled.) The duration is 20 hours. Thanks.

Power is proportional to square of voltage when resistance is constant (P = V^2 / R). And a resistive heater is such a system. So here, time increases four-fold, not two-fold. The time is still 40 hrs, not 20 hrs.