Question

11.2. A steel rod has a length of exactly 0.2 cm at
30°C. What will be its lenght at 60°C?
(Ans: 0.20066 cm).
Solution

Answer 1

BTS AND EXO LIVE FOREVER AND EVER

Answer 2

Given:

A steel rod has a length of exactly 0.2 cm at

30°C.

To find:

Length of the rod at 60° C.

Calculation:

Metallic solids have a property of expanding with increase in temperature such that it follows an equation:

$\therefore \: \rm L_{new} = L + \Delta L$

The term ∆L can be represented in terms of temperature , linear expansion coefficient :

$= > \: \rm L_{new} = L + L \alpha \Delta \theta$

$= > \: \rm L_{new} = L(1 + \alpha \Delta \theta)$

Putting the values in SI unit:

$= > \: \rm L_{new} = 0.2 \bigg \{1 + (12 \times {10}^{ - 6} )\times (60 - 30) \bigg \}$

$= > \: \rm L_{new} = 0.2 \bigg \{1 + (12 \times {10}^{ - 6} )\times 30 \bigg \}$

$= > \: \rm L_{new} = 0.2 \bigg \{1 + (12 \times {10}^{ - 5} )\times 3 \bigg \}$

$= > \: \rm L_{new} = 0.2 \bigg \{1 + (36 \times {10}^{ - 5} ) \bigg \}$

$= > \: \rm L_{new} = 0.2 \bigg \{1 + 0.00036 \bigg \}$

$= > \: \rm L_{new} = 0.2 \bigg \{1.00036 \bigg \}$

$= > \: \rm L_{new} = 0.200072 \: cm$

• I have taken the value of $\alpha$ as 12 × 10^(-6) /°C.

So, final length is 0.200072 cm.