Question 287: Thermodynamics & KTG

Question

A solid metallic cube having total surface area 24 m
2
is uniformly heated. If its temperature is increased by 10$^\circ$C, calculate the increase in volume of the cube. (Given $\alpha$ = 5.0 $	imes$ 10
$-$4
$^\circ$C
$-$1
).

Accepted Answer

$6 	imes {l^2} = 24$
$ \Rightarrow l = 2$ m
$	herefore$ ${{\Delta V} \over V} = 3 	imes {{\Delta l} \over l}$
$ \Rightarrow \Delta V = 3 	imes (\alpha \Delta T) 	imes V$
$ = 3 	imes 5 	imes {10^{ - 4}} 	imes 10 	imes (8)$
$ = 120 	imes {10^{ - 3}}$ m
3
$ = 120 	imes {10^{ - 3}} 	imes {10^6}$ cm
3
$ = 1.2 	imes {10^5}$ cm
3

Answer

2.4 $	imes$ 10
6
cm
3

Answer

1.2 $	imes$ 10
5
cm
3

Answer

6.0 $	imes$ 10
4
cm
3

Answer

4.8 $	imes$ 10
5
cm
3

Thermodynamics & KTG

A solid metallic cube having total surface area 24 m 2 is uniformly heated. If its temperature is increased by 10^\circC, calculate the increase in volume of the cube. (Given \alpha = 5.0 \times 10 -4 ^\circC -1 ).

Choose the correct answer: