A brass measuring rule is correct at 15degree celcius the volume obtained where the length of an object is measured with rule at 35degree celcius appears to be 841.4cm. What is the length of the object (linear expansivity of brass=1.8×10raise to power of 5 degree celcius per one
metre)?
The length of the object is 841.4 cm / (1 + (1.8 x 10^5 x (35 - 15))/1000000) = 841.2 cm.
Well, that's quite a mouthful! Let's see if we can figure it out together, shall we?
First, let me make sure I understand the problem correctly. We have a brass measuring rule that's correct at 15 degrees Celsius. The volume obtained when measuring the length of an object with the rule at 35 degrees Celsius appears to be 841.4 cm. We also know that the linear expansivity of brass is 1.8 × 10^5 degree Celsius per one... one what, though? I'm assuming you meant "per one meter" since we're dealing with lengths.
Now, to find the length of the object, we need to take into account the thermal expansion of the rule. We can use the formula:
ΔL = αLΔT
Where ΔL is the change in length, α is the linear expansivity of the material, L is the original length, and ΔT is the change in temperature.
In this case, we want to find the original length, L. So we need to rearrange the formula:
L = ΔL / (αΔT)
However, we don't have the actual change in length or the change in temperature. All we have is the volume obtained. So, without more information, it's not possible to determine the length of the object using the given data.
I apologize for not being able to give you a definitive answer. It seems like this problem might need some additional information. But hey, at least we had a chance to exercise our brain a bit, right?
To find the length of the object, we can use the concept of linear expansivity and the formula:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the linear expansivity of brass
L is the initial length of the object
ΔT is the change in temperature
Given:
α = 1.8 x 10^(-5) °C^(-1) (linear expansivity of brass)
L = ?
ΔT = 35 °C - 15 °C = 20 °C
ΔL = 841.4 cm (change in length)
We can rearrange the formula to solve for L:
ΔL = α * L * ΔT
L = ΔL / (α * ΔT)
Substituting the given values:
L = 841.4 cm / (1.8 x 10^(-5) °C^(-1) * 20 °C)
L ≈ 234067.57 cm (rounded to two decimal places)
Therefore, the length of the object is approximately 234067.57 cm.
To find the length of the object, we need to take into account the thermal expansion of brass. The linear expansivity of brass, as given in the question, is 1.8 x 10^(-5) degree Celsius per degree Celsius.
Let's denote the initial length of the object as L1 and the final length as L2. We are given the initial temperature (15 degrees Celsius), the final temperature (35 degrees Celsius), and the apparent volume (841.4 cm^3).
First, we need to calculate the change in temperature:
ΔT = T2 - T1
= 35°C - 15°C
= 20°C
Next, we use the formula for linear thermal expansion:
ΔL = α * L1 * ΔT
where α is the linear expansivity of brass (1.8 x 10^(-5) °C^(-1)), L1 is the initial length, and ΔT is the change in temperature.
Now, we rearrange the formula to solve for L2:
L2 = L1 + ΔL
Substituting the values we know:
L2 = L1 + (α * L1 * ΔT)
= L1 + (1.8 x 10^(-5) * L1 * 20)
Finally, we substitute the given apparent volume into the formula for volume:
V = L2^3
841.4 cm^3 = (L1 + (1.8 x 10^(-5) * L1 * 20))^3
Now we can solve this equation to find L1, the initial length of the object.