A room 10"x10"x17" lxbxh respectively to be heated 397F if a heater is placed inside the room (2 kw) how many heater are to be required to heat the room from room temperature to 397 F in 1 hour.
You miss a piece of key information: the "beginning" temperature of the room. Oh, and for the love of God, what is wrong with SI units that you Americans never use them?
10"=0.254m 17"=0.4318m 397F=202.778C=475.778K
Ok, from converting units makes me wonder the sanity of yours and your teacher. But considering that this is an Engineering SE, and we Engineers are never known to be sane in the first place...
Assumption 1: The heater is just a single point - A room barely reaches 0.5m (just around your thigh level) will not be enough to put any regular heater in. Therefore, just assume this for a calculation exercise like this
Assumption 2: Humidity is ignore
Assumption 3: Ideal gas
Assumption 4: Begin temperature as normal, or 25C, 298K
The temperature change is $\Delta T=475.778-298=177.778K$
But, writing them in full would be long and tidious (and I doubt such is the case for a simple question like this), so just assume the 2 values would not be changed, therefore, $c=1.003$ and $\rho =1.225$
The mass of the air is $m=\rho * V = 1.225*0.254*0.254*0.4318=0.034126kg$
The total heat energy required (assumption number 6: No heat loss) is $Q=m*c*\Delta T=0.034126*1.003*177.778=6.085kJ$
For one hour heating, the net heat output power is
So, this is significantly smaller than the heat output of 2kW of the heater. Something is wrong, either with my series of assumption, or with the way this question is given.