A copper kettle contains water at 24.2 °C. When the water is heated to 87.3 °C, the volume of the kettle expands by 7.34 x 10-5 m3. Determine the volume of the kettle at 24.2 °C.
Ah, the tale of the expanding kettle! Well, fear not, dear human, for Clown Bot is here to assist you with a dash of humor.
To determine the volume of the kettle at 24.2 °C, we need to consider the expansion of the kettle due to the change in temperature.
Now, let's call the initial volume of the kettle at 24.2 °C V1, and the final volume after it's heated to 87.3 °C V2. The change in volume can be calculated using the formula:
ΔV = V2 - V1
Given that ΔV is 7.34 x 10-5 m3, we can rearrange the formula to solve for V1:
V1 = V2 - ΔV
Substituting the given values, we get:
V1 = V2 - 7.34 x 10-5 m3
However, we still need to find V2, the volume of the kettle at 87.3 °C. In order to do that, we need to know the coefficient of volume expansion (β) of the kettle.
So, my dear human, without the missing information, I'm afraid all I can do is make you chuckle with silly jokes. How about this one: Why couldn't the bicycle find its way home? Because it lost its bearings!
To determine the volume of the kettle at 24.2 °C, we can use the coefficient of volume expansion for copper.
The equation for linear expansion is given by:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length
ΔT is the change in temperature
For volume expansion, the equation becomes:
ΔV = β * V * ΔT
Where:
ΔV is the change in volume
β is the coefficient of volume expansion
V is the original volume
ΔT is the change in temperature
Now, let's calculate the change in volume using the provided information:
ΔT = 87.3 °C - 24.2 °C = 63.1 °C
ΔV = 7.34 x 10^(-5) m^3
We can rearrange the equation to solve for the original volume V:
V = ΔV / (β * ΔT)
Next, we need to find the coefficient of volume expansion for copper. The coefficient of volume expansion for most solids, including copper, is approximately three times the coefficient of linear expansion. Let's assume the coefficient of linear expansion for copper is α_copper = 16.8 x 10^(-6) °C^(-1).
Hence, the coefficient of volume expansion for copper is:
β_copper = 3 * α_copper = 3 * 16.8 x 10^(-6) °C^(-1)
Now we can calculate the volume of the kettle at 24.2 °C:
V = ΔV / (β_copper * ΔT)
V = 7.34 x 10^(-5) m^3 / (3 * 16.8 x 10^(-6) °C^(-1) * 63.1 °C)
To determine the volume of the kettle at 24.2 °C, we can use the principle of thermal expansion. The change in volume of an object due to a change in temperature can be calculated using the coefficient of volume expansion (β) and the initial and final temperatures.
The formula for calculating the change in volume is as follows:
ΔV = β * V * ΔT
Where:
- ΔV is the change in volume
- β is the coefficient of volume expansion
- V is the initial volume
- ΔT is the change in temperature
In this case, we know the change in temperature (ΔT) is 87.3 °C - 24.2 °C = 63.1 °C, and the change in volume (ΔV) is 7.34 x 10^-5 m^3.
To find the coefficient of volume expansion (β), we need to refer to a table or look up the value for copper. The coefficient of volume expansion for copper is approximately 5.10 x 10^-5 °C^-1.
Now we have all the information we need to determine the initial volume (V) of the kettle. Rearranging the formula, we have:
V = ΔV / (β * ΔT)
Plugging in the values, we get:
V = 7.34 x 10^-5 m^3 / (5.10 x 10^-5 °C^-1 * 63.1 °C)
Now we can calculate the volume of the kettle at 24.2 °C.
changeinVolume=orgVolume*coeffvolumeexpansion*deltaTemp
where the coefficient of volume expansion is 3*coefficentlinearexpansionCu = 3*16.1E-6