Question

A brass rod of cross section $2cm \times 2cm$ is heated through $10^\circ C$ and prevented from expansion. The thermal force exerted on the clamp is:
(For brass, $\alpha = 2 \times {10^{ - 5}}/^\circ C$ and $Y = 2 \times {10^{10}}Pa$)
(A) $160N$
(B) $1600N$
(C) $100N$
(D) $8000N$

Answer 1

Thermal kinetic energy of a body is the total kinetic energy of motion of all the particles of the body that make up the body. Thermal force is thermal stress. Use the formula of thermal force and substitute the given values to solve the question.

Formula Used: $F = YA\alpha \Delta T$
Where,
$F$ is thermal force
$A$ is area of cross section
$Y$ is young’s modulus
$\Delta T$ is the change in temperature
$\alpha$ is the coefficient linear expansion

Complete step by step answer: Thermal stress is the stress of the body going through thermal expansion, a resultant internal force is formed which generates a particle stress. That kind of stress is called thermal stress or force.
Thermal force is given by
$F = YA\alpha \Delta T$
$F$ is thermal force
$\Delta T =$ change in temperature
$\alpha$ is the coefficient linear expansion
$A$ is area of cross section
$Y$ is young’s modulus
By substituting the given values in the above formula, we get
$F = (2 \times {10^{10}}) \times (4 \times {10^{ - 4}}) \times 2 \times {10^{ - 5}} \times 10$
By simplifying it, we get
$= 8 \times {10^6} \times (2 \times {10^4})$ $\left( {\because {a^m}{a^n} = {a^{m + n}}} \right)$
$\Rightarrow F = 1600N$
Hence, the thermal force on the clamp is $1600N$.
Therefore, from the above explanation, the correct answer is, option (B) $1600N$

Note: Thermal force is not always applied to expand the body. It can also be applied for the contraction of the body. Since force is a vector quantity, expansion of the body is represented by a positive sign and the contraction is shown by a negative sign. For this question, it was important to know the formula of thermal force to solve the question.