The density of water at 20°C is 998 kg/m3 and at 40°C 992 kg/m3 . The coefficient of volume expansion of water is

Question

The density of water at 20°C is 998 kg/m3 and at 40°C 992 kg/m3 . The coefficient of volume expansion of water is (A)  3 × 10-4 ° C (B)  2 × 10-4 ° C (C)  6 × 10-4 ° C (D)  10-4 ° C

Tardigrade Admin · Accepted Answer

(a): As P Ts = ( PT1/1+ &gamma; Δ T) = ( PT1/ 1+ &gamma; ( T2-T1)) Here, T1= 20 ° C, T2 = 40 ° C P20 = 998 kg / m3 , P40 = 992 kg / m3 ∴ 992 = (998/ 1+&gamma; (40-20)) 992= (998/ 1+ 20 &gamma;) 992(1+20&gamma;) = 998 1+ 20 &gamma; = (998/992) -1 = (6/992) &gamma; = (6/992) × (1/20)= 3 × 10-4 / ° C

Q. The density of water at $2 0^{\circ} C$ is $998 k g / m^{3}$ and at $4 0^{\circ} C$ $992 k g / m^{3}$ . The coefficient of volume expansion of water is

$3 \times 1 0^{- 4}^{\circ} C$

$2 \times 1 0^{- 4}^{\circ} C$

$6 \times 1 0^{- 4}^{\circ} C$

$1 0^{- 4}^{\circ} C$

Q. The density of water at 20∘C is 998kg/m3 and at 40∘C 992kg/m3. The coefficient of volume expansion of water is

3×10−4∘C

2×10−4∘C

6×10−4∘C

10−4∘C

(a) : As PTs​=1+γΔTPT1​​=1+γ(T2​−T1​)PT1​​ Here,T1​=20∘C,T2​=40∘C P2​0=998kg/m3,P4​0=992kg/m3 ∴992=1+γ(40−20)998​ 992=1+20γ998​ 992(1+20γ)=998 1+20γ=992998​−1=9926​ γ=9926​×201​=3×10−4/∘C

Q. The density of water at $2 0^{\circ} C$ is $998 k g / m^{3}$ and at $4 0^{\circ} C$ $992 k g / m^{3}$ . The coefficient of volume expansion of water is

$3 \times 1 0^{- 4}^{\circ} C$

$2 \times 1 0^{- 4}^{\circ} C$

$6 \times 1 0^{- 4}^{\circ} C$

$1 0^{- 4}^{\circ} C$