A compartment measures 3 meters by 5 meters and is 2.8 meters high. A fire raises the temperature from 20 degrees C to 1000 C. If the starting temperature assuming the compartment remains closed?

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To determine the starting temperature of the compartment assuming it remains closed, we need to make certain assumptions and use the principles of heat transfer.

First, we need to assume that the compartment is an enclosed system without any heat loss or gain except through the walls. In reality, some heat may escape through various means, but for the purposes of this calculation, we will ignore such losses.

We can use the principle of heat transfer, specifically the formula for heat conduction, to solve this problem. The formula is given by:

Q = mcΔT

where:
Q is the heat transferred,
m is the mass of the compartment,
c is the specific heat capacity of the material, and
ΔT is the change in temperature.

In this case, we assume that the compartment has a constant mass, and we know the specific heat capacity of air at constant pressure is approximately 1005 J/(kg·°C).

First, let's calculate the heat transfer (Q) required to raise the temperature of the compartment:

Q = mcΔT

The mass (m) of the compartment can be calculated by multiplying the volume by the density of air. The density of air at around room temperature and atmospheric pressure is approximately 1.2 kg/m³.

Volume (V) = length × width × height = 3 m × 5 m × 2.8 m = 42 m³
Mass (m) = Volume × Density = 42 m³ × 1.2 kg/m³ = 50.4 kg

Next, we calculate the change in temperature (ΔT) using the starting (T1) and final (T2) temperatures:

ΔT = T2 - T1 = 1000 °C - 20 °C = 980 °C

Now that we have the mass of the compartment and the change in temperature, we can calculate the heat transfer (Q):

Q = mcΔT = 50.4 kg × 1005 J/(kg·°C) × 980 °C

Calculating this expression will give us the heat transfer required to raise the temperature of the compartment. However, we need to convert this value into a usable unit, such as calories or kilocalories. We can use the conversion factor of 1 calorie = 4.184 J.

Once we have the heat transfer in calories, we can calculate the starting temperature (T1) using the formula:

T1 = T2 - (Q / m / c)

Calculate the value of Q and convert it into calories using the conversion factor. Then, substitute the values into the formula to find the starting temperature.