Increase in length per unit length per degree rise in temperature of an aluminum rod of 10m is 24x10^-6/C. what would be the increase in volume per unit volume per degree rise in temperature of a cube of aluminum of volume 100cm3. when both are heated through the same range of temperature
To calculate the increase in volume per unit volume per degree rise in temperature, we need to use the coefficient of thermal expansion, which gives the increase in length per unit length per degree rise in temperature.
Given that the increase in length per unit length per degree rise in temperature (α) for an aluminum rod is 24x10^-6/C, we can use this value to calculate the change in volume.
The formula to calculate the change in volume per unit volume per degree rise in temperature (β) is given by:
β = 3α
Where β is the volume coefficient of thermal expansion and α is the linear coefficient of thermal expansion.
Since a cube has three dimensions, the volume coefficient of thermal expansion is three times the linear coefficient of thermal expansion.
Let's calculate the volume coefficient of thermal expansion for the aluminum rod first:
β = 3α
β = 3 * 24x10^-6/C
β = 72x10^-6/C
Now, we can calculate the increase in volume per unit volume per degree rise in temperature for the cube of aluminum.
Given that the initial volume of the cube (V_initial) is 100 cm^3, we can calculate the increase in volume (ΔV) using the formula:
ΔV/V_initial = β * ΔT
Where ΔV is the change in volume, V_initial is the initial volume, β is the volume coefficient of thermal expansion, and ΔT is the change in temperature.
Let's assume the change in temperature (ΔT) is the same for both the aluminum rod and the aluminum cube. Plug in the values:
ΔV/V_initial = (72x10^-6/C) * ΔT
ΔV/V_initial = (72x10^-6) * ΔT
Now, we can find the actual increase in volume by multiplying both sides of the equation by V_initial:
ΔV = (72x10^-6) * ΔT * V_initial
Plug in the given value of V_initial (100 cm^3) to get the final result:
ΔV = (72x10^-6) * ΔT * 100 cm^3
Therefore, the increase in volume per unit volume per degree rise in temperature of the cube of aluminum is (72x10^-6) * ΔT * 100 cm^3.