Calculating Thermal Energy from Passive Solar Heater

[tofulemon]

This is for a physics finals project. So it's not really a homework question. But I didn't know where else to post it and I need immediate help.
I have made a passive solar heater out of pop cans and I need to find out how much energy (thermal) is produced. I know the equation for thermal energy is Q=m.c.ΔT. The problem is I can't exactly calculate the mass of air going in. I could find mass by using the density formula m=ρ.v, but then that leaves finding volume. But then, you also can't exactly calculate how much volume air can hold. So I was advised to calculate the flow rate of air using this equation Q = A.v where v is velocity. But I wasn't sure how the flow rate of air be equal to volume and come out as thermal energy (in joules).

Here's some details about my box frame.
my box is 2'x4' using 2"x4" wood (3.5"x1.5" in real life). so the volume of my box is 21"x45"x3.5" = 3307.5 cubic meter. I have 2 holes cut with a diameter of 4.5" so the radius would be 2.25"

now what I don't know is how to obtain mass.
Can someone please explain to me what I'm doing wrong and guide me to determine the thermal energy coming out of this solar heater..

Homework Statement

What is the equation to calculate thermal energy coming out of the solar heater ?

ΔT = 0.5-1 degree C every 5 minutes ( I collected temperatures for 2 hours every 5 minutes and they ranged from 34-42 degrees C)
c = 1.006 kJ/kgC
ρ of air = 1.165 kg/m³ at 30 degrees C
volume of box = 3307.5 cubic meter
r = 2.25"

Homework Equations

Et = m.c.ΔT (general equation)
Q = A.v where v is velocity and Q is flow rate
m=ρ.v (density equation, solving for mass)

The Attempt at a Solution

If I assume that the flow rate is equal to volume then my equations should be something like this:

Et = m.c.ΔT (general equation)
= (ρ.v).c.ΔT (subbed in density multiplied by volume for mass)
= (ρ(A.v)).c.ΔT (subbed in flow rate equation for volume , which I think is wrong but right)
= (ρ(pr.r^2)(v)).c.ΔT (worked everything out and this is what I get)

See where I'm going with this? I don't fully understand it. And I'm not sure how to calculate velocity either without using some sort of instrument that just shoots out a value.

Unit check:
kg/m^3 . m^2 . m/s . KJ/Kg K . K
I have done a unit check and after manipulating common variables I get KJ .s
Is this correct?

I don't need to get a specific value in the end. I just need to check if my variables are correct and if it's the right equations I'm using and if my final answer will come out as joules.
If there's anything I'm missing. please let me know.
Thanks.

 

[KataKoniK]

Hello,

Thank you for reaching out for help with your physics finals project. It sounds like you have made a great start with your passive solar heater made out of pop cans. Let's take a look at your equations and see if we can help you find the equation to calculate the thermal energy coming out of your solar heater.

First, let's review the equation for thermal energy: Q = m.c.ΔT, where Q is the thermal energy in joules, m is the mass in kilograms, c is the specific heat capacity in joules per kilogram per degree Celsius, and ΔT is the change in temperature in degrees Celsius.

In order to calculate the thermal energy coming out of your solar heater, you will need to determine the mass of air that is flowing through it. You mentioned that you were advised to calculate the flow rate of air using the equation Q = A.v, where A is the cross-sectional area of the opening and v is the velocity of the air. This is a good approach, but you will also need to know the density of air in order to calculate the mass of air flowing through the heater.

To find the density of air, you can use the ideal gas law: PV = nRT, where P is the pressure in pascals, V is the volume in cubic meters, n is the number of moles of gas, R is the gas constant (8.314 joules per mole per Kelvin), and T is the temperature in Kelvin. Rearranging this equation to solve for density (ρ = n/V), we get ρ = P/RT.

Now, let's look at your specific project details. You have a box frame with dimensions 2'x4' using 2"x4" wood. The volume of your box is 21"x45"x3.5" = 3307.5 cubic meters. You also have two holes cut with a diameter of 4.5", giving a radius of 2.25".

To calculate the cross-sectional area of the openings, we can use the formula for the area of a circle: A = πr^2. Plugging in the radius of 2.25", we get A = 3.14(2.25)^2 = 15.9 square inches.

Next, we need to convert the units from square inches to square meters. There are 1550 square inches in 1