# NCERT Class 11 Physics Solutions: Chapter 11 – Thermal Properties of Matter-Part 3

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**Question 11.6:**

A steel tape long is correctly calibrated for a temperature of . The length of a steel rod measured by this tape is found to be on a hot day when the temperature is . What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is ? Coefficient of linear expansion of steel .

**Answer:**

Length of the steel tape at temperature ,

At temperature T1 = 45°C, the length of the steel rod,

Coefficient of linear expansion of steel,

Let be the actual length of the steel rod and l' be the length of the steel tape at

Hence, the actual length of the steel rod measured by the steel tape at can be calculated as:

Therefore, the actual length of the rod at . Its length at

**Question 11.7:**

A large steel wheel is to be fitted on to a shaft of the same material. At the outer diameter of the shaft is and the diameter of the central hole in the wheel is . The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: αsteel

**Answer:**

The given temperature can be written in kelvin as:

Outer diameter of the steel shaft at

Diameter of the central hole in the wheel at

Coefficient of linear expansion of steel,

After the shaft is cooled using ‘dry ice’, its temperature becomes

The wheel will slip on the shaft, if the change in diameter,

Temperature can be calculated from the relation:

Therefore, the wheel will slip on the shaft when the temperature of the shaft is

**Question 11.8:**

A hole is drilled in a copper sheet. The diameter of the hole is at . What is the change in the diameter of the hole when the sheet is heated to ? Coefficient of linear expansion of copper

**Answer:**

Initial temperature,

Diameter of the hole at

Final temperature,

Diameter of the hole at

Co-efficient of linear expansion of copper,

For co-efficient of superficial expansion and change in temperature, we have the relation:

But

Change in diameter

Hence, the diameter increases by