Question 423: Thermodynamics & KTG

Question

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $\alpha $/
o
C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $\Delta $TK. Young's modulus, Y, for this metal is :

Accepted Answer

We know,
Young's Modulus, Y = ${{Stress} \over {Strain}}$
Stress = ${F \over A}$
Strain = ${{\Delta l} \over l}$
$ 	herefore $  Y =  ${{{F \over A}} \over {{{\Delta l} \over l}}}$
We also know,
$l$
f
= $l$
i
(1 + $\alpha $$\Delta $T)
$ \Rightarrow $   $l$
f
=  $l$
i
+  $l$
i
$\alpha $$\Delta $T
$ \Rightarrow $   ${{{l_f} - {l_i}} \over {{l_i}}}$  =  $\alpha $$\Delta T$
$ \Rightarrow $   ${{\Delta l} \over {{l_i}}}$ = $\alpha $$\Delta $T
$ 	herefore $   y  =  ${{{F \over A}} \over {\alpha \Delta T}}$
=  ${F \over {A\alpha \Delta T}}$

Answer

${F \over {A\alpha \Delta T}}$

Answer

${F \over {A\alpha (\Delta T - 273)}}$

Answer

${F \over {2A\alpha \Delta T}}$

Answer

${{2F} \over {A\alpha \Delta T}}$

Thermodynamics & KTG

Choose the correct answer: