Question 318: Properties of Matter

Question

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in tmperature. The length of aluminium rod is : ($$\alpha $$Cu = 1.7 × 10–5 K–1 and 
 $$\alpha $$Al = 2.2 × 10–5 K–1)

Accepted Answer

At any temperature
$${\left( {\Delta l} ight)_{Cu}} = {\left( {\Delta l} ight)_{Al}}$$
$${l_{Cu}}{\alpha _{Cu}}\Delta T = {l_{Al}}{\alpha _{Al}}\Delta T$$
$$ \Rightarrow $$ 88 $$ 	imes $$ 1.7 $$ 	imes $$ 10
-5
= $${l_{Al}}$$ $$ 	imes $$ 2.2 ÃÂ 10
Ã¢ÂÂ5
$$ \Rightarrow $$ $${l_{Al}}$$ = 68 cm

Answer

119.9 cm

Answer

88 cm

Answer

68 cm

Answer

6.8 cm

Properties of Matter

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in tmperature. The length of aluminium rod is : ($\alpha Cu = 1.7 × 10–5 K–1 and \alpha $Al = 2.2 × 10–5 K–1)

Choose the correct answer: