How much time require to heat?

  • Thread starter blazerman
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In summary, the conversation was about trying to find the amount of time it would take to heat a specific volume of air from 35°C to 1000°C using a 1400 watt heater. There were some discrepancies in the calculations due to using the incorrect specific heat and assumptions about the volume being constant.
  • #1
blazerman
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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

 
Last edited:
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  • #2
Did you use Cp instead of Cv?
 
  • #3
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?
 
  • #4
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
 
  • #5
What is constant? Pressure or volume?
 
  • #6
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.
 

1. How much time does it take to heat water?

The time it takes to heat water depends on several factors, including the volume of water, the initial temperature, and the power of the heating source. Generally, it takes about 4-5 minutes for a standard 8 oz. cup of water to reach boiling point on a stovetop.

2. How long does it take to heat a room?

The time it takes to heat a room varies depending on the size of the room, the insulation, and the heating system. On average, it takes 15-30 minutes for a room to reach a comfortable temperature with central heating, while it may take longer with a space heater.

3. How much time does it take to heat food in a microwave?

The time it takes to heat food in a microwave depends on the type of food, the quantity, and the wattage of the microwave. As a rule of thumb, it takes about 1-2 minutes to heat a small portion of food (1 cup) and 2-3 minutes for a larger portion (2 cups) on high power.

4. How long does it take for a hair straightener to heat up?

The time it takes for a hair straightener to heat up varies depending on the model and brand. On average, it takes 30-60 seconds for a flat iron to reach the desired temperature, which is usually indicated by a light or beep.

5. How much time do electric blankets take to heat up?

The time it takes for an electric blanket to heat up depends on the size, settings, and insulation of the blanket. Generally, it takes about 10-20 minutes for an electric blanket to reach a comfortable temperature, but it may take longer for larger or thicker blankets.

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