How do we Calculate Temperature & Time of Heating Element

In summary, To calculate the temperature and time of a heating element made with SWG 16 wire, with specific resistivity = 1.45 ohms-mm-3, density = 7.1 gm-cm-3, resistance = 0.685 ohms/Meter, and weight = 15 Gram/Meter, we can use the formula P = I2R to determine the energy delivered in 1 hour for a 2.5 kW element or 3.5 kW element. To calculate the temperature raised in 1 hour, we can use the formula P = I2R * 3600 s. To calculate the heat generated in 1 hour, we can use the formula P = I2R
  • #1
blazerman
4
0
How do we Calculate Temperature & Time of Heating Element

Heating Wire having the following Data :
SWG 16(1.63mm)
Specific Resistivity = 1.45 ohms-mm-3
Density = 7.1 gm-cm-3
Resistance = 0.685 ohms/Meter
Weight = 15 Gram/Meter

(a)In order to Build Heating Element using the above wire for Making 2.5 KiloWatt heating Element
(b)In Order to Build Heating Element using the above wire for Making 3.5 KiloWatt heating Element

Take ambient & room temperature as 35 degree Centrigrade.
How to Calculate the following :
(a)Formula for Calculating Temperature Raised in 1 hour ?
or alternately What would be temperature of heating element after Heating Element heated for 1 Hour?

(b)Formula for Calculating, How Many Calories of Heat in generated in 1 hour?
(c)Say if the Temperature is raised till (i)800 degree Centigrade what would be the Kilowatt generated & in what time this Temperature would be raised?

(c)Say if the Temperature is raised till (ii)1000 degree Centigrade what would be the Kilowatt generated & in what time this Temperature would be raised?

Please state the explanation using formulas.
 
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  • #2
Well energy is just power * time.

So the energy delivered by the heating 2.5 kW heating element is just 2.5 kW*3600 s, and that delievered by the 3.5 kW element is 3.5 kW*3600 s.

Formula for Calculating Temperature Raised in 1 hour ?
Now is one supposed to calculate the heating of the room?

If the heat transfer is steady-state, can one use radiative heat transfer equation?
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html#c2

The power radiated depends on the current and resistance of the wire = P = I2R.
 
  • #3


(a) The formula for calculating the temperature raised in 1 hour is:
ΔT = (P*R*t)/(m*C)
Where:
ΔT = change in temperature
P = power (in watts)
R = resistance (in ohms)
t = time (in seconds)
m = mass (in grams)
C = specific heat capacity (in J/g-K)

To calculate the temperature of the heating element after 1 hour, we can use the formula:
T = T0 + ΔT
Where:
T = final temperature
T0 = initial temperature
ΔT = change in temperature calculated using the formula above.

For a 2.5 kilowatt heating element:
ΔT = (2500*0.685*3600)/(15*7.1*1.45) = 71.24°C
T = 35 + 71.24 = 106.24°C

For a 3.5 kilowatt heating element:
ΔT = (3500*0.685*3600)/(15*7.1*1.45) = 99.73°C
T = 35 + 99.73 = 134.73°C

(b) The formula for calculating the heat generated in 1 hour is:
Q = P*t
Where:
Q = heat generated (in Joules)
P = power (in watts)
t = time (in seconds)

For a 2.5 kilowatt heating element:
Q = (2500*3600) = 9,000,000 Joules

For a 3.5 kilowatt heating element:
Q = (3500*3600) = 12,600,000 Joules

(c) (i) To calculate the kilowatt generated when the temperature is raised to 800°C, we can use the formula:
P = (m*C*ΔT)/t
Where:
P = power (in watts)
m = mass (in grams)
C = specific heat capacity (in J/g-K)
ΔT = change in temperature (in K)
t = time (in seconds)

For a 2.5 kilowatt heating element:
P = (15*0.24*800)/3600 = 0.133 kilowatts

For a 3.5 kilowatt heating element:
P = (15*0.24*800
 

1) How does the type of heating element affect temperature and heating time?

The type of heating element used can greatly impact the temperature and heating time. Different materials have different thermal conductivity, which affects how quickly and efficiently heat is transferred to the surrounding environment. For example, a copper heating element will heat up faster and reach higher temperatures compared to a stainless steel heating element of the same size and power. Therefore, the type of heating element used must be taken into consideration when calculating temperature and heating time.

2) What factors besides the heating element type influence temperature and heating time?

Aside from the type of heating element, other factors that can affect temperature and heating time include the power output of the heating element, the size and shape of the heating element, the ambient temperature, and the starting temperature of the object being heated. These factors must be considered in addition to the heating element type to accurately calculate temperature and heating time.

3) How do we calculate the temperature of a heating element?

To calculate the temperature of a heating element, several variables must be known, including the power output of the heating element, the thermal conductivity of the heating element material, the size and shape of the heating element, and the ambient temperature. With these variables, the temperature can be calculated using the appropriate mathematical formula or by using a thermal modeling software.

4) Is there a standard formula for calculating heating time?

There is no standard formula for calculating heating time, as it can vary depending on the specific heating element and the object being heated. However, there are general guidelines and equations that can be used to estimate heating time, such as the heat transfer equation and the specific heat equation. It is important to also consider factors such as heat loss and thermal mass when calculating heating time.

5) How can we ensure accurate temperature and heating time calculations?

To ensure accurate temperature and heating time calculations, it is important to have precise and reliable measurements of the variables involved, such as the power output of the heating element and the starting temperature of the object being heated. It is also essential to use the appropriate equations or thermal modeling software, considering all relevant factors, and to double-check calculations for any errors or inconsistencies.

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