What wil be the new area of 400cm square of a solid,if its temperature is raised by 10k.(L.E=19times 10raised to power 2
To find the new area of a solid when its temperature is raised, we need to consider the linear expansion coefficient (L.E) and the original area.
Given:
Original area (A) = 400 cm²
Linear expansion coefficient (L.E) = 19 × 10²
Let's calculate the change in area (ΔA) first:
ΔA = L.E * A * ΔT, where ΔT is the change in temperature.
Given:
ΔT = 10 K (Kelvin)
Substituting the values:
ΔA = (19 × 10²) * (400 cm²) * (10 K)
Calculating:
ΔA = 760,000 cm² K
To find the new area (A'), we add the change in area (ΔA) to the original area (A):
A' = A + ΔA
Substituting the values:
A' = 400 cm² + 760,000 cm² K
Simplifying:
A' = 760,400 cm²
Therefore, the new area of the solid, when its temperature is raised by 10 K, will be 760,400 cm².
To determine the new area of a solid when its temperature is raised, we need to use the linear expansion equation:
ΔA = α * A * ΔT
Where:
ΔA is the change in area
α is the coefficient of linear expansion
A is the initial area
ΔT is the change in temperature
Given:
Initial area (A) = 400 cm^2
Change in temperature (ΔT) = 10 K
Coefficient of linear expansion (α) = 19 * 10^(-2)
Now, let's substitute the given values into the equation and solve for ΔA:
ΔA = (19 * 10^(-2)) * (400 cm^2) * (10 K)
First, let's simplify the unit of area to simplify the calculation. Since 1 cm^2 is equivalent to 10^(-4) m^2:
A = 400 cm^2 * (10^(-4) m^2/1 cm^2)
A = 40 m^2
Now, let's substitute the simplified values:
ΔA = (19 * 10^(-2)) * (40 m^2) * (10 K)
Calculating:
ΔA = (19 * 10^(-2)) * (40 m^2) * (10 K)
ΔA = 7.6 m^2 * 10 K
ΔA = 76 m^3 * K
Thus, the change in area (ΔA) is 76 m^3 * K.
To find the new area, we add this change to the initial area:
New area = Initial area + ΔA
New area = 400 cm^2 + 76 m^3 * K
Note: Please ensure that the units are consistent throughout the calculation. In this case, the initial area is given in cm^2, and the final unit is m^2.