Question

an iron rod is 2.58m long at 0°c. calculate the length of a brass rod at 0°c if the difference between the length of the two rods must remain the same at all temperatures. ( linear expansivity of iron= 1.2 ×10^-5k^-1, linear expansivity of brass= 1.9 × 10^-5k^-1)​

Answer 1

1.63 m

Step-by-step explanation:

difference between the length of iron rod and brass rod must remain same, writing it in the equation form

`l_(iron) - l_(brass) = C`

where C is a constant, differentiation both sides with respect to temperature(
`\theta`),

`(dl_(iron))/(d\theta) - (dl_(brass))/(d\theta) = 0` ... (1)

According to linear expansion equation,

`(dl)/(d\theta) = \alpha l_0`

where
`l_0` is the length at 0 degree Celsius.

Now,

substituting values in equation 1 we get,

`\alpha_(iron). l_(iron) - \alpha_(brass) . l_(brass) = 0`

substituting the values of respective coefficient and length of iron at 0 degree Celsius we get,

`l_(brass) = 1.63` m

Hopefully, this answer helped you solve the question!