A metal cube of length 10.0 mm at 0° C (273 K ) is heated to 200° C (473 K ). Given: its coefficient of linear expansion is 2 × 10-5 K -1. The percent change of its volume is

Question

A metal cube of length 10.0 mm at 0° C (273 K ) is heated to 200° C (473 K ). Given: its coefficient of linear expansion is 2 × 10-5 K -1. The percent change of its volume is (A) 0.1 (B) 0.2 (C) 0.4 (D) 1.2

Tardigrade Admin · Accepted Answer

(Δ V/V)=&gamma; ⋅ Δ T=3 α Δ T=3(2 × 10-5 K -1)(200 K ) =12 × 10-3 (Δ V/V)= 12 × 10-3 × 100 %=1.2 %

Q. A metal cube of length 10.0 mm at $0^{\circ} C (273 K)$ is heated to $20 0^{\circ} C (473 K)$ . Given: its coefficient of linear expansion is $2 \times 1 0^{- 5} K^{- 1}$ . The percent change of its volume is

0.1

0.2

0.4

1.2

$\frac{Δ V}{V} = γ \cdot Δ T = 3 α Δ T = 3 (2 \times 1 0^{- 5} K^{- 1}) (200 K)$
$= 12 \times 1 0^{- 3} \frac{Δ V}{V} = 12 \times 1 0^{- 3} \times 100% = 1.2%$

Q. A metal cube of length 10.0 mm at 0∘C(273K) is heated to 200∘C(473K). Given: its coefficient of linear expansion is 2×10−5K−1. The percent change of its volume is

0.1

0.2

0.4

1.2

VΔV​=γ⋅ΔT=3αΔT=3(2×10−5K−1)(200K) =12×10−3VΔV​=12×10−3×100%=1.2%

Q. A metal cube of length 10.0 mm at $0^{\circ} C (273 K)$ is heated to $20 0^{\circ} C (473 K)$ . Given: its coefficient of linear expansion is $2 \times 1 0^{- 5} K^{- 1}$ . The percent change of its volume is

$\frac{Δ V}{V} = γ \cdot Δ T = 3 α Δ T = 3 (2 \times 1 0^{- 5} K^{- 1}) (200 K)$
$= 12 \times 1 0^{- 3} \frac{Δ V}{V} = 12 \times 1 0^{- 3} \times 100% = 1.2%$