The coefficient of volume expansion of glycerine is 49× 10- 5K- 1 . The fractional change in its density for a 30° C rise in temperature will be

Question

The coefficient of volume expansion of glycerine is 49× 10- 5K- 1 . The fractional change in its density for a 30° C rise in temperature will be (A) 1.45× 10- 2 (B) 2× 10- 4 (C) 3.5× 10- 3 (D) 2.5× 10- 2

Tardigrade Admin · Accepted Answer

Let V0 be the initial volume of glycerine, i.e, at 0° C (dry). If Vt be its volume at 30° C Then Vt=V0(1 + &gamma; Δ t) = V0(1 + 49 × (10)- 5 × 30) Vt=V0(1 + 0.01470)=1.01470 V0 ⇒ (V0/Vt)=(1/1.01470) Let ρ o and ρ t be the initial and final densities of glycerine then initial density, ρ 0=(m/V0) and final density, ρ t=(m/Vt) Where, m= mass of glycerine (Δ ρ /ρ 0)= fractional change in the density ((ρ )t - (ρ )0/(ρ )0)=(m ((1/Vt) - (1/V0))/(m)V0)=((V0/Vt) - 1) (Δ ρ /(ρ )0)=((1/1.01470) - 1)=-0.0145 Here, negative sign shows that density decreases with rise in temperature |(Δ ρ /ρ 0)|=0.0145=1.45× 10- 2

Q. The coefficient of volume expansion of glycerine is $49 \times 1 0^{- 5} K^{- 1}$ . The fractional change in its density for a $3 0^{\circ} C$ rise in temperature will be

$1.45 \times 1 0^{- 2}$

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

$3.5 \times 1 0^{- 3}$

$2.5 \times 1 0^{- 2}$

Q. The coefficient of volume expansion of glycerine is 49×10−5K−1 . The fractional change in its density for a 30∘C rise in temperature will be

1.45×10−2

2×10−4

3.5×10−3

2.5×10−2

Q. The coefficient of volume expansion of glycerine is $49 \times 1 0^{- 5} K^{- 1}$ . The fractional change in its density for a $3 0^{\circ} C$ rise in temperature will be

$1.45 \times 1 0^{- 2}$

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

$3.5 \times 1 0^{- 3}$

$2.5 \times 1 0^{- 2}$