Question

Question #73f4e

Answer 1

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 `lambdaand alpha` as below

`sigma_x=alpha lambda (T−T_"ref")`
where `T` is uniform temperature of the solid metal sample and `T_"ref"` is reference temperature, say room temperature.