# NCERT Class 11 Physics Solutions: Chapter 11 – Thermal Properties of Matter-Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for CBSE/Class-8 right from your home: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-8.

**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