Miran Fernando
Mechanical
- Jun 16, 2023
- 19
Hello everybody,
I would like feedback please on a large discrepancy between a theoretical calculation and an experimental measurement I have taken.
I ran a 470 Ohm 5 Watt ceramic (at 50 V and 0.1 A, both confirmed using a multimeter) resistor inside of an 8 litre insulated cooler box and measured the air temperature (two thermocouples used, both in close agreement) over time. The resistor was suspended inside of the box and was not in contact with the sides or bottom. I also had a DC fan blowing air across the resistor in an effort to make sure heat is being transferred out of the ceramic element and into the air.
If I calculate the amount of energy needed to raise the temperature of air from 26 °C to 31 °C:
Q = m∙cp∙ΔT
Where:
Q is energy provided by the resistor (Joules),
m is the mass of the air in the box, 0.0095 (kg),
cp is the specific heat capacity of air, 1006 (J / (kg∙K))
ΔT is the change in temperature, 5 (°C)
After converting 8 litres to 0.008 m^3 and multiplying by air density of 1.184 (kg / m^3) I get around 0.0095 kg.
So to change the temperature of air by 5 °C (from 26 °C to 31 °C):
Q = (0.0095) * (1006) * (31 - 26) = 47.8 J
In the experiment it took 15 minutes (900 seconds) for the air to heat from 26 °C to 31 °C. 5 Watts multiplied by 900 seconds is 4500 Joules. So I calculated that it would take roughly 50 J to heat the air by a certain amount. But the experiment required nearly 95 times the amount of energy.
The only two explanations I have are that:
1. The box is not a very effective insulator and leaks quickly. Though the sides of the box felt cool to the touch during the experiment. If energy were conducting through the material, I should be able to feel the box warming up.
2. Some of the energy produced by the resistor goes into heating a) the ceramic body of the resistor itself, b) the interior material of the box. b) does not seem very likely to me as the resistor is hanging in the air.
I’m not sure what I am doing wrong, but would appreciate feedback and advice.
My reason for doing this test is because I would like to be able to put some electronics inside the box, power them and calculate how much heat they are dissipating based on the temperature that I measure. But I am now unsure if that will be reliable based on these results.
I would like feedback please on a large discrepancy between a theoretical calculation and an experimental measurement I have taken.
I ran a 470 Ohm 5 Watt ceramic (at 50 V and 0.1 A, both confirmed using a multimeter) resistor inside of an 8 litre insulated cooler box and measured the air temperature (two thermocouples used, both in close agreement) over time. The resistor was suspended inside of the box and was not in contact with the sides or bottom. I also had a DC fan blowing air across the resistor in an effort to make sure heat is being transferred out of the ceramic element and into the air.
If I calculate the amount of energy needed to raise the temperature of air from 26 °C to 31 °C:
Q = m∙cp∙ΔT
Where:
Q is energy provided by the resistor (Joules),
m is the mass of the air in the box, 0.0095 (kg),
cp is the specific heat capacity of air, 1006 (J / (kg∙K))
ΔT is the change in temperature, 5 (°C)
After converting 8 litres to 0.008 m^3 and multiplying by air density of 1.184 (kg / m^3) I get around 0.0095 kg.
So to change the temperature of air by 5 °C (from 26 °C to 31 °C):
Q = (0.0095) * (1006) * (31 - 26) = 47.8 J
In the experiment it took 15 minutes (900 seconds) for the air to heat from 26 °C to 31 °C. 5 Watts multiplied by 900 seconds is 4500 Joules. So I calculated that it would take roughly 50 J to heat the air by a certain amount. But the experiment required nearly 95 times the amount of energy.
The only two explanations I have are that:
1. The box is not a very effective insulator and leaks quickly. Though the sides of the box felt cool to the touch during the experiment. If energy were conducting through the material, I should be able to feel the box warming up.
2. Some of the energy produced by the resistor goes into heating a) the ceramic body of the resistor itself, b) the interior material of the box. b) does not seem very likely to me as the resistor is hanging in the air.
I’m not sure what I am doing wrong, but would appreciate feedback and advice.
My reason for doing this test is because I would like to be able to put some electronics inside the box, power them and calculate how much heat they are dissipating based on the temperature that I measure. But I am now unsure if that will be reliable based on these results.
