A glass window with a mass of 20kg is heated to a temperature of 32C by the sun. How much thermal energy is released by the window to the surroundings as it cools to 5C at night?
The answer is 4.5x10^5 J but I don't know how to get there. Thank you!
△T=T2-T1
△T=5-32
△T=-27°C
m=20kg
c = 8.4 x10^2
△T=-27°C
Q=mc△T
Q=(20)(8.4x102)(-27)
Q=-4.5x10^5J
The negative sign indicates that heat is being lost by the glass window. When the temperature decreases, heat flows out of the object into its surroundings. Since heat lost is a negative quantity, the result will also be negative, indicating the amount and direction of heat flow.
why is there a negative by the 27
Well, it seems like this window really knows how to "cool" down! Let's calculate the amount of thermal energy released.
To calculate the thermal energy released, we can use the formula:
Q = mcΔT
Where:
Q is the thermal energy released (in joules),
m is the mass of the window (in kg),
c is the specific heat capacity of glass (approximately 840 J/kg*C), and
ΔT is the change in temperature (in Celsius).
In this case, the initial temperature of the window is 32°C, and it cools down to 5°C at night. So, ΔT is:
ΔT = 5°C - 32°C = -27°C
We use -27°C because the temperature change is a decrease. Now we can plug the values into the formula:
Q = (20 kg) * (840 J/kg°C) * (-27°C)
When we calculate this, we get:
Q ≈ -4.536 × 10^5 J
As we're looking for the amount of energy released, we don't really want a negative value. So, we can take the absolute value of Q:
|Q| ≈ 4.536 × 10^5 J
And since we're dealing with significant figures, let's round the answer to two significant figures:
Q ≈ 4.5 × 10^5 J
And there you have it! The amount of thermal energy released by the window is approximately 4.5 × 10^5 J.
To calculate the amount of thermal energy released by the window as it cools down, we can use the formula:
Q = mcΔT
Where:
Q is the thermal energy released
m is the mass of the window
c is the specific heat capacity of the material (glass)
ΔT is the change in temperature (final temperature - initial temperature)
In this case, we are given:
m = 20 kg (mass of the window)
c = unknown (specific heat capacity of glass)
ΔT = (5°C - 32°C) = -27°C (change in temperature)
To find the specific heat capacity of glass, we need additional information or make an assumption.
Assuming the specific heat capacity of glass is around 840 J/(kg·°C), which is a common value for glass, we can substitute the values into the formula:
Q = mcΔT
Q = (20 kg)(840 J/(kg·°C))(-27°C)
Q = -453,600 J ≈ -4.54 ×10^5 J
It is important to note that the negative sign indicates that energy is being released by the window (as it cools down). However, the value of energy is usually stated as a positive value, so we will take the absolute value of Q:
|Q| = |-453,600 J| = 453,600 J ≈ 4.54 × 10^5 J
Therefore, based on the assumption that the specific heat capacity of glass is around 840 J/(kg·°C), the thermal energy released by the window as it cools to 5°C is approximately 4.54 × 10^5 J.
heat=massglass*specificheatglass* (32-5)
△T=T2-T1
△T=32-5
△T=27°C
m=20kg
c = 8.4 x10^2
△T=27°C
Q=mc△T
Q=(20)(8.4x102)(-27)
Q=-4.5x10^5J