The linear expansivity of a material of a cube is 12×10^-1/k if the length of each side of the cube is 10cm find the area of one face of the cube when it's temperature is raised by 30k
The linear expansivity (α) is given by the formula:
α = ΔL / (L * ΔT)
where ΔL is the change in length, L is the original length, and ΔT is the change in temperature.
In this case, the linear expansivity (α) is 12 × 10^-1 / K, ΔT is 30 K, and L is 10 cm.
We can rearrange the formula to solve for ΔL:
ΔL = α * L * ΔT
ΔL = (12 × 10^-1 / K) * (10 cm) * (30 K)
ΔL = 36 cm
Since the cube has equal length for all sides, the change in length will be the same for all sides. Therefore, the length of each side of the cube increased by 36 cm.
The new length of each side is 10 cm + 36 cm = 46 cm.
To find the area of one face of the cube, we can use the formula:
Area = (length of one side)^2
Area = (46 cm)^2
Area = 2116 cm^2
Therefore, the area of one face of the cube, when its temperature is raised by 30 K, is 2116 cm².
To find the area of one face of the cube after the temperature is raised by 30K, we need to use the formula for linear expansion:
ΔL = α * L0 * ΔT
Where:
ΔL = Change in length
α = Linear expansivity
L0 = Original length
ΔT = Change in temperature
Given:
Linear expansivity (α) = 12 × 10^-1/K
Original length (L0) = 10 cm
Change in temperature (ΔT) = 30 K
Let's substitute these values into the formula to find ΔL:
ΔL = (12 × 10^-1/K) * (10 cm) * (30 K)
ΔL = 12 * 10^-1 * 10 * 30 cm
Now, we can calculate ΔL:
ΔL = 360 cm
Since the cube has equal sides, the change in length (ΔL) will be the same for all sides. Therefore, each side of the cube will have a change in length of 360 cm.
The new length of each side can be found by adding the change in length to the original length:
New length = L0 + ΔL
New length = 10 cm + 360 cm
New length = 370 cm
Since the cube is made up of equal squares on each face, the area of one face of the cube is:
Area = (new length)^2
Area = (370 cm)^2
Area = 136900 cm²
Therefore, the area of one face of the cube when its temperature is raised by 30K is 136900 cm².