Question 878: Thermodynamics & KTG

Question

The side of a copper cube is $$1 \mathrm{~m}$$ at $$0^{\circ} \mathrm{C}$$. What will be the change in its volume, when it is heated to $$100^{\circ} \mathrm{C}$$ ? $$\left[\alpha_{	ext {copper }}=18 	imes 10^{-6} /{ }^{\circ} \mathrm{C}ight]$$

Accepted Answer

The side length of a copper cube is $1 \, 	ext{m}$ at $0^{\circ} 	ext{C}$. We need to determine the change in its volume when it is heated to $100^{\circ} 	ext{C}$. Given the coefficient of linear expansion for copper $\left(\alpha_{	ext{copper}}ight)=18 	imes 10^{-6} /{}^{\circ} 	ext{C}$, we use the volumetric expansion formula for a cube:
$ \Delta V = V \cdot 3\alpha \cdot \Delta T $
Insert the given values:
$ \Delta V = 3 	imes 18 	imes 10^{-6} 	imes 100 $
This simplifies to:
$ \Delta V = 54 	imes 10^{-4} \, 	ext{m}^3 $

Answer

$$45 	imes 10^{-4} \mathrm{~m}^3$$

Answer

$$54 	imes 10^{-4} \mathrm{~m}^3$$

Answer

$$34 	imes 10^{-4} \mathrm{~m}^3$$

Answer

$$64 	imes 10^{-4} \mathrm{~m}^3$$

Thermodynamics & KTG

The side of a copper cube is $1 \mathrm{~m} at 0^{\circ} \mathrm{C}. What will be the change in its volume, when it is heated to 100^{\circ} \mathrm{C} ? \left[\alpha_{\text {copper }}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right]

Choose the correct answer: