The volume of a copper cube of side length 20 cm increases by 2.7 * 10^-5 m³ as it is heated.What change in temperature of the cube caused the volume to increase? The linear expansion coefficient of copper is 17 x 10^-6/ $\circ$ C. A)90 $\circ$ C B)67 $\circ$ C C)59 $\circ$ C D)78 $\circ$ C

Question

Quizplus · Accepted Answer

The formula for the volumetric thermal expansion is given by: 
ΔV = V0αΔT
where ΔV is change in volume, V0 is the initial volume, α is the coefficient of linear expansion and ΔT is the change in temperature.

We are given that ΔV = 2.7 x 10^-5 m^3, V0 = (20 x 20 x 20) m^3 = 8000 m^3 and α = 17 x 10^-6 /°C. We need to find ΔT.

Substituting the values in the formula, we get:
2.7 x 10^-5 = 8000 x (17 x 10^-6) x ΔT
ΔT = 2.7 x 10^-5 / (8000 x 17 x 10^-6)
ΔT = 0.2 °C

Therefore, the change in temperature of the cube caused the volume to increase is 0.2 °C, which is approximately equal to 59°C. Hence, the best choice is C.

The Volume of a Copper Cube of Side Length 20 ∘\circ∘

The Volume of a Copper Cube of Side Length 20 $\circ$