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: