How Long to Heat Air from 35°C to 1000°C with a 1400W Heater?

[blazerman]

Homework Statement

A Heating Element rated 1400Watt Supply 220V
Current : 6.36 Amperes
Resistance = 34.57 Ohms

Area to be heated L X B X H = 4inches X 4inches X 9inches

From Temperature 35 Deg.C to 1000 Deg.C

All under standard/normal pressure
2. Relevant Question
How long would it take to heat from 35 Deg.C to 1000 Deg.C

The Attempt at a Solution

Joules = Mass(Kg) X Heat Capacity on kJ/Kg.DegC X Delta T

Inch(s) -> to Meter(s)
4 -> 0.1016
4 -> 0.1016
9 -> 0.2286


Therefore Volume of Air = 0.00235974 Mt^3

Density of Air @ 35. Deg C = 1.1455 Kg/Mt^3

Amount of Air @ 35. Deg C = 0.00235974 X 1.1455 = 0.0027031 Kg

Heat Capacity of Air = 1.06 kJ/kg Deg.C

Delta T = 1000 - 35 = 965 Deg.C

Joules to be consumed = 0.0027031 x 1.06 X 965 = 2.76499 kJ = 2764.99 Joules

Joules = Current^2 X resistance X time(Seconds)

Then 27466.99 = (6.36)^2 X 34.57 X T(Seconds)
or, T = 1.97 Seconds (Something is wrong)


Time=? (to raise the temperature from 35 Deg.C to 1000 Deg.C)

The Attempt at a Solution

 

[LawrenceC]

Did you use Cp instead of Cv?

 

[Emilyjoint]

your 'joules to be consumed'... 2764.99 does not match the Joules (27466.99) on the next line.
Is this a typing mistake you have made?

 

[blazerman]

Correct is 2764.99
As 2.76499 kJ converted to Joules as 2764.99

So help me how to find out the correct time as the time required cannot be 1.97secs

 

[voko]

What is constant? Pressure or volume?

 

[LawrenceC]

Your problem says nothing about a flow so one has to assume it is a fixed volume. Given that, you need constant volume specific heat rather than constant pressure specific which it seems you are using. The result will be less energy required so less time to heat.

Are you sure you have the box dimensions correct. Placing a 1400 watt heater in a 4X4X9 inch box seems like overkill. This sounds like a toaster-oven to me which would take longer to heat because of the mass of the heating element and the ceramic core it is generally wound around.