A teel Tyre diametre i 150cm at 10°c to what temperature mut the Tyre be heated to jut fit the wheel (take linear expanivity of teel a=11×10-6 k-1)
To determine the temperature to which the Tyre needs to be heated in order to fit the wheel, we can use the concept of thermal expansion.
First, let's calculate the change in diameter of the Tyre due to the change in temperature. The formula for linear expansion is given as:
ΔL = α * L * ΔT
Where:
ΔL is the change in length or diameter
α is the linear expansivity coefficient
L is the initial length or diameter
ΔT is the change in temperature
In this case, we are looking for the change in temperature (ΔT), so we rearrange the formula as follows:
ΔT = ΔL / (α * L)
Given that the initial diameter (L) is 150 cm and the linear expansivity coefficient (α) for steel is 11 * 10^(-6) K^(-1), we need to determine the change in diameter (ΔL) to find ΔT.
From the question, it's mentioned that the Tyre needs to fit the wheel, which implies that the final diameter of the Tyre should be the same as that of the wheel. Therefore, the change in diameter can be calculated as:
ΔL = final diameter - initial diameter
= L_wheel - L
Assuming the diameter of the wheel is the same as the initial diameter of the Tyre (150 cm), we substitute these values into the formula:
ΔL = 150 cm - 150 cm
= 0 cm
Now, the equation becomes:
ΔT = 0 cm / (11 * 10^(-6) K^(-1) * 150 cm)
Since ΔL is zero, this means that there is no change in diameter, implying that the Tyre just needs to be at the initial temperature of 10°C to fit the wheel.