Question

An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of 15°C. Both rods have the same diameter. The rods are now joined end-to-end to form a rod 90.0 cm long. If the temperature is now raised from 15°C to 90°C, what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is 2.4 × 10-5 K-1 and that of steel is 1.2 × 10-5 K-1.

Answer 1

Answer:

0.9 cm

Explanation:

The computation in the increase in the length of the joined rod is shown below:

As we know that

Increase in length = increase in the length of aluminum rod + increase in The length of steel rod

$= 10cm \times 2.4e - 5\times (90-15) + 80cm\times 1.2e - 5\times (90-15)$

= 0.9 cm

We simply added the length of aluminium rod and length of steel rod so that the length of the joined rod could come and the same is to be considered  

Answer 2

We have that for the Question, it can be said that

the increase in the length of the joined rod

$\triangle L= 0.9cm$

From the question we are told

An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of 15°C. Both rods have the same diameter.

The rods are now joined end-to-end to form a rod 90.0 cm long.

If the temperature is now raised from 15°C to 90°C,

what is the increase in the length of the joined rod?

The coefficient of linear expansion of aluminum is 2.4 × 10-5 K-1 and that of steel is 1.2 × 10-5 K-1.

Generally the equation for the change length  is mathematically given as

$\triangle L=change in L of aluminium rod +change in L of steel rod\\\\Therefore\\\\\triangle L= 10*2.4*10^{-5}*(90-15) + 80cm*1.2*10^{-5}*(90-15)\\\\\triangle L= 0.9cm$

Hence

the increase in the length of the joined rod

$\triangle L= 0.9cm$

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