Question

An iron vat is 14 m long at room temperature (20°C). How much longer is it when it contains boiling water at 1 atm pressure? answer in M

Answer 1

Step-by-step explanation:

It is given that,

Length of iron bar, l = 14 m

Room temperature, T = 20° C

Pressure, P = 1 atm

The change in length due to change in temperature is called linear expansion. It is given by :

`\Delta l=l\alpha \Delta T`

`\alpha` is the coefficient of linear expansion,
`\alpha =12* 10^(-6)\ C^(-1)`

We know that the boiling temperature of water T' = 100° C

`\Delta l=l\alpha (T'-T)`

`\Delta l=14* 12* 10^(-6)* (100-20)`

`\Delta l=0.0134\ m`

So, the new length of the iron rod is,
`L=14\ m+0.0134\ m=14.013\ m`

Hence, this is the required solution.

Answer 2

The length after elongation is 0.1243 m

Solution:

As per the question;

Length of the iron vat, L = 14 m

Temperature, T =
`20^(\circ)` = 293 K

Temperature at 1 atm, T' =
`100^(\circ)` = 373 K

Pressure, P = 1 atm

Thermal expansion coefficient,
`\alpha = 11.1* 10^(- 6)/^(\circ)C`

Now,

Change in length is given by:

`\Delta L = \alpha L\Delta T`

`L' - L = \alpha L\Delta T`

`L' = L(1 + \alpha L\Delta T)`

`L' = 14(1 +  11.1* 10^(- 6)(100 - 80)`

L' = 0.1243 m