Question

What is the volume of a lead ball at 40.00°C if the ball's volume at 78.00°C is 51.00 cm^3? Give your answer to four significant figures. The linear expansion coefficient of lead is 29.00 x 10^- /Cº.

Answer 1

Answer:$50.831 cm^3$

Explanation:

Given

Volume of lead ball is $51 cm^3$

Linear expansion  coefficient of lead is $29\times 10^{-6}/^{\circ}C$

We know $V=V_0\left ( {1+\gamma \left ( \Delta T\right )}\right )$

Where $V_0$ initial volume

$\gamma$=Volume expansion coefficient

$\Delta T$=change in temperature

and $\gamma =3\alpha$

$V_{70}=V_{40} \left ( 1+\gamma \left ( 78-40\right )\right )$

$51=V_{40}\left ( 1+87\times 10^{-6}\left ( 38\right )\right )$

$V_{40}=\frac{51}{1.003306}$

$V_{40}=50.831 cm^3$