# Question 73f4e

Aug 28, 2017

Lets first of all understand Young's modulus of a substance. It is also called modulus of elasticity and is a measure of the stiffness of a solid material.

In other words it is a number that measures resistance of an object to being deformed elastically when a stress is applied to the object. Elastic modulus $\lambda$ is defined as

 λ -= "stress"/ "strain"
where stress is the force causing the deformation, and strain is the ratio of the change in value of a particular parameter to its original value.

Since strain is a dimensionless quantity, λ has units of stress.

Now, we know that amount of thermal expansion of any solid is related to its coefficient of linear expansion $\alpha$. We can therefore, estimate/calculate thermal stress produced in a particular direction say $x$-direction as σ_x by combining both $\lambda \mathmr{and} \alpha$ as below

sigma_x=alpha lambda (T−T_"ref")#
where $T$ is uniform temperature of the solid metal sample and ${T}_{\text{ref}}$ is reference temperature, say room temperature.