Question

Two rods of same length and same diameter are drawn from equal masses and same quantity of heat is supplied to the two rods find the ratio of expansion if specific heats of the materials is (2/3) and that of coefficient of linear expansion is (1/2)

• A. $4/3$
• B. $1/2$
• C. $3/4$
• D. $1/3$

Answer 1

Answer: (C)

$3/4$

Heat given $\Delta H=ms\Delta \theta$

$⟹\Delta H\propto s\Delta \theta$

We get $s_1\Delta {\theta }_1=s_2\Delta {\theta }_2$

Also, change in length $\Delta l=l\alpha \Delta \theta$

And, $\frac{\Delta l_1}{\Delta l_2}=\frac{{\alpha }_1\Delta {\theta }_1}{{\alpha }_2\Delta {\theta }_2}=\frac{{\alpha }_1}{{\alpha }_2}\times \frac{s_2}{s_1}=\frac{1}{2}\times \frac{3}{2}=\frac{3}{4}$