a brass cube of size 10cm is heated through 30 degree. if the linear expansivity of brass is 2.0*10^-5 k^-1. what is the increase in its volume?

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Physics

To find the increase in volume of the brass cube, we need to use the equation for volumetric expansion, which is given by:

∆V = V₀ * β * ∆T

Where:
∆V is the change in volume
V₀ is the initial volume
β is the coefficient of volumetric expansion
∆T is the change in temperature

Given:
Initial size of the cube (side length) = 10 cm
Linear expansivity of brass (α) = 2.0 * 10^(-5) K^(-1)
Change in temperature (∆T) = 30 °C

First, we need to calculate the initial volume of the cube:

V₀ = (side length)³

V₀ = (10 cm)³ = 1000 cm³

Next, we can calculate the change in volume using the formula:

∆V = V₀ * β * ∆T

∆V = 1000 cm³ * (2.0 * 10^(-5) K^(-1)) * 30 °C

Now, let's do the calculation:

∆V = 1000 cm³ * (2.0 * 10^(-5) K^(-1)) * 30 °C
∆V = 6000 * 10^(-5) cm³ K^(-1) °C
∆V = 0.06 cm³ K^(-1) °C

Therefore, the increase in volume of the brass cube when heated through 30 °C is approximately 0.06 cm³.

K = 30 + 273.15 = 303.15o Kelvin

(2*10^-5/K)*303.15K*10cm = 0.06063 cm Increase in Length, each side.

(0.06063)^3 = 2.2288*10^-4 cm^3 Increase in Volume.

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