Question 352: Thermodynamics & KTG

Question

Two different wires having lengths L
1
and L
2
,
and respective temperature coefficient of linear
expansion $$\alpha $$
1
and $$\alpha $$
2
, are joined end-to-end.
Then the effective temperature coefficient of
linear expansion is :

Accepted Answer

L'
1
= L
1
(1 + $$\alpha $$
1
$$\Delta $$T)
L'
2
= L
2
(1 + $$\alpha $$
2
$$\Delta $$T)
L'
eq
= (L
1
+ L
2
) (1 + $$\alpha $$
avg
$$\Delta $$T)
$$ 	herefore $$ (L
1
+ L
2
) (1 + $$\alpha $$
avg
$$\Delta $$T) = L
1
(1 + $$\alpha $$
1
$$\Delta $$T) + L
2
(1 + $$\alpha $$
2
$$\Delta $$T)
$$ \Rightarrow $$ (L
1
+ L
2
)$$\alpha $$
avg
= L
1
$$\alpha $$
1
+ L
2
$$\alpha $$
2
$$ \Rightarrow $$ $$\alpha $$
avg
= $${{{\alpha _1}{L_1} + {\alpha _2}{L_2}} \over {{L_1} + {L_2}}}$$

Answer

$$2\sqrt {{\alpha _1}{\alpha _2}} $$

Answer

$$4{{{\alpha _1}{\alpha _2}} \over {{\alpha _1} + {\alpha _2}}}{{{L_2}{L_1}} \over {{{\left( {{L_2} + {L_1}} \right)}^2}}}$$

Answer

$${{{\alpha _1} + {\alpha _2}} \over 2}$$

Answer

$${{{\alpha _1}{L_1} + {\alpha _2}{L_2}} \over {{L_1} + {L_2}}}$$

Thermodynamics & KTG

Two different wires having lengths L 1 and L 2 , and respective temperature coefficient of linear expansion $\alpha 1 and \alpha $ 2 , are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

Choose the correct answer: