Question

What is the increase in length of a steel bar 10 m long if its temperature is increased from 20°C to 70°C? (The coefficient of linear expansion of steel is 12x10^-6/°C).

a) 0.0054 m

b) 0.006 m

c) 0.054 m

d) 0.6 m

Answer 1

The increase in length of a 10 m long steel bar when its temperature is increased from 20°C to 70°C is 0.006 m, using the coefficient of linear expansion for steel.

Step-by-step explanation:

To calculate the increase in length of a steel bar due to an increase in temperature, the formula for linear thermal expansion is used:

\(\Delta L = \alpha \times L \times \Delta T\), where:

• • \(\Delta L\) is the change in length.
  • \(\alpha\) is the coefficient of linear expansion of steel, which is \(12 \times 10^{-6}\) per degree Celsius (°C).
  • \(L\) is the original length of the steel bar.
  • \(\Delta T\) is the change in temperature.

In this case, we have:

• • \(\alpha = 12 \times 10^{-6} /°C\)
  • \(L = 10\) meters
  • \(\Delta T = 70°C - 20°C = 50°C\)

Plugging these values into the formula gives:

\(\Delta L = 12 \times 10^{-6} /°C \times 10\) m \(\times 50°C = 0.006\) m

Therefore, the correct increase in length of the steel bar when the temperature is increased from 20°C to 70°C is 0.006 meters (option b).