HI!can anyone help me please, just on part b.Thank you so much.
A spherical steel ball bearing has a diameter of 2.540 cm at 23°C.
(a) What is the diameter when its temperature is raised to 94°C?
___ cm
(b) What temperature change is required to increase its volume by 0.9%?
____°C I need help on part b only, Thank again.
what is the initial volume? What is the coefficent of volume expansion for steel?
Use the equation to find new volume, then find diameter.
b) same technique, you know the volume change.
Sure! I can help you with part b of the question.
To find the temperature change required to increase the volume of the steel ball bearing by 0.9%, we need to use the formula for volume change due to temperature:
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 want to find ΔT, so we can rearrange the equation:
ΔT = ΔV / (β * V)
Given that the volume change is 0.9% (or 0.009 in decimal form) and the ball bearing is a sphere, we can use the formula for the volume of a sphere:
V = (4/3) * π * r³
Since we are given the initial diameter, we need to first calculate the initial radius:
Initial radius (r) = initial diameter / 2
Now, let's substitute the values into the equation:
ΔT = ΔV / (β * V)
ΔT = ΔV / (β * (4/3) * π * r³)
We need to know the coefficient of volume expansion (β) for steel. This value can be found in a physics or materials science reference book. For steel, the coefficient of volume expansion is approximately 0.000012 per °C.
Now, we have all the values needed to calculate ΔT. Let's proceed with the calculations:
1. Calculate the initial volume (V):
V = (4/3) * π * (r_initial)^3
2. Calculate the change in volume (ΔV):
ΔV = V * 0.009
3. Calculate ΔT:
ΔT = ΔV / (β * V)
Plug in the values you obtained from steps 1 and 2 to calculate ΔT, which will give you the temperature change required to increase the volume by 0.9%.
I hope this explanation helps! If you have any further questions, feel free to ask.