Question #73f4e

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Question #73f4e

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Answer 1 · 2017-08-28T20:03:50

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 $λ$ $lambda$ 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.

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