First slide

Thermal expansion

Question

The density of water at $20 ° C is 998 kg / m^{3}$ and $40 ° C 992 k g / m^{3}$ . The coefficient of volume expansion of water is

Easy

A

$3 \times 10^{- 4} / {}^{\circ}C$
B

$2 \times 10^{- 4} / {}^{\circ}C$
C

$6 \times 10^{- 4} / {}^{\circ}C$
D

$10^{- 4} / {}^{\circ}C$

Solution

$As ρ_{T_{2}} = \frac{ρ_{T_{1}}}{(1 + γ Δ T)} = \frac{ρ_{T_{1}}}{1 + γ (T_{2} - T_{1})} Here, T_{1} = 20 ° C, T_{2} = 40 ° C ρ_{20} = 998 kg / m^{3}, ρ_{40} = 992 kg / m^{3} ∴ 992 = \frac{998}{1 + γ (40 - 20)} 992 = \frac{998}{1 + 20 γ} 992 (1 + 20 γ) = 998 1 + 20 γ = \frac{998}{992} or 20 γ = \frac{998}{992} - 1 = \frac{6}{992} γ = \frac{6}{992} \times \frac{1}{20} = 3 \times 10^{- 4} / {}^{\circ}C$

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