Calculate the change of volume that occure when a steel bearing with an initial volume of 1.8cm^3 is heated from 20°C to 80°C.
Tried to use the formula DeltaV/Vinitial=Beta×DeltaT but kept getting the wrong answer though my maths could be off?
so, show us your numbers, and maybe we can tell what went wrong.
I got DeltaV=(1/12×10^-6k)(80-20)(1.8cm^3)
=1.296×10^-3cm^-3
The answer Im supposed to be getting is 3.9×10^-3cm^-3?
for steel coef of VOLUMETRIC expansion is
about 33 *10^-6 to 39*10^-6 depending on composition of the steel. You used I suspect 1.13 *10^-6 which is more like the LINEAR coef
To calculate the change in volume of an object due to thermal expansion, you can use the formula:
ΔV = V₀ * β * ΔT
Where:
ΔV is the change in volume
V₀ is the initial volume
β is the coefficient of volumetric expansion
ΔT is the change in temperature
In this case, you correctly used the formula ΔV/V₀ = β * ΔT, but it seems there might be an error elsewhere. Let's go step by step to find the correct answer:
1. Before proceeding with the calculation, you need to ensure that you have the correct coefficient of volumetric expansion (β) for steel. The value of β can differ based on the type of steel. However, a commonly used average value is around 0.000012 per °C (in SI units).
2. Now, we can substitute the given values into the formula:
V₀ = 1.8 cm³ (initial volume)
ΔT = 80°C - 20°C = 60°C (change in temperature)
β = 0.000012 per °C (coefficient of volumetric expansion for steel)
ΔV = 1.8 cm³ * 0.000012 per °C * 60°C
= 0.01296 cm³
Therefore, the change in volume when the steel bearing is heated from 20°C to 80°C is approximately 0.01296 cm³.