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`

Step-by-step explanation:

Given

Volume of lead ball is
`51 cm^3`

Linear expansion coefficient of lead is
`29* 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* 10^(-6)\left ( 38\right )\right )`

`V_(40)=(51)/(1.003306)`

`V_(40)=50.831 cm^3`