Does a resistor in an AC circuit produce the same heat as in a DC circuit?

Does a 1k ohm resistor produce the same heat in a AC circuit which has an rms voltage of 10 volts (60 hz.) as it would in a 10 volt DC circuit?

Answer

Edit

This answers the original version of the question, which asked,

Does a 1k ohm resistor produce the same heat in a AC circuit which has an average voltage of 10 volts (60 hz.) as it would in a 10 volt DC circuit?

No, the heat produced depends on V², not V.

As a simple example, consider a sinusoidal AC signal with 10 V peak to peak, and 0 DC component. The average voltage is zero, but it still delivers power to the resistor and the resistor still heats up.

To get the heat produced in the AC circuit to be the same as in the DC circuit, you want the rms voltage (The square root of the mean of the square of the voltage) in the AC circuit to be equal to the DC voltage in the DC circuit.

Edit: As D34dman points out in his answer, there are some special cases where the rms voltage and average voltage happen to work out to the same value.