Answer :
The temperature needs to be increased by approximately 0.0118 °C for the bronze sleeve to slip over the steel cylinder. Thus, the correct option is A) 0.028°C.
The temperature increase required for the bronze sleeve to slip over the steel cylinder can be found using the concept of thermal expansion.
The difference in diameters between the inside diameter of the sleeve and the outside diameter of the cylinder determines the amount of expansion needed for them to fit together.
Let's denote:
- d_bronze as the inside diameter of the bronze sleeve
- d_steel as the outside diameter of the steel cylinder
Given:
- α_B = 16.9 × 10^(-6) /°C (coefficient of linear expansion for bronze)
- α_S = 11.9 × 10^(-6) /°C (coefficient of linear expansion for steel)
- d_bronze = 99.8 mm = 0.0998 m
- d_steel = 100 mm = 0.1 m
The change in diameter needed for the sleeve to slip over the cylinder is given by:
Δd = d_steel - d_bronze
Δd = 0.1 - 0.0998
Δd = 0.0002 m
The temperature increase required for this change in diameter can be calculated using the formula:
ΔT = Δd / α
For bronze:
ΔT = 0.0002 / 16.9 × 10^(-6)
ΔT ≈ 0.0118 °C
Therefore, the temperature must be increased by approximately 0.0118 °C for the bronze sleeve to slip over the steel cylinder.
**Correct Option:** A) 0.028°C
Complete Question:
A bronze (αB = 16.9 × 10-6 /°C) sleeve with an inside diameter of 99.8 mm is to be placed over a solid steel (αS = 11.9 × 10-6 /°C) cylinder that has an outside diameter of 100 mm. If the temperatures of the cylinder and sleeve remain equal, how much must the temperature be increased in order for the bronze sleeve to slip over the steel cylinder?
Options:
A) 0.028°C
B) 0.032°C
C) 0.036°C
D) 0.040°C
Correct Option:*
A) 0.028°C