The coefficient of volume expansion of a liquid is 49 × 10-5 K -1. When temperature is raised by 30° C, then which of the following statement is correct?

Question

The coefficient of volume expansion of a liquid is 49 × 10-5 K -1. When temperature is raised by 30° C, then which of the following statement is correct? (A) Its density decreases. (B) Its density increases. (C) Its fractional decrease in density is 2.5 × 10-2. (D) Its fractional increase in density is 2.5 × 10-2.

Tardigrade Admin · Accepted Answer

Variation of density with temperature is given by

ρ^{'} = \frac{ρ}{1 + α _{V} Δ θ}

where,

ρ =

density at given temperature
and

ρ^{'} =

density at unknown temperature.
So, its density decreases with temperature.
Fractional decrease is

\frac{ρ ^{'} - ρ}{ρ} = (\frac{1}{1 + 49 \times 1 0 ^{- 5} \times 30} - 1) = 1.5 \times 1 0^{- 2}

Thus, the statement given in option is correct, rest are incorrect.

Q. The coefficient of volume expansion of a liquid is $49 \times 1 0^{- 5} K^{- 1}$ . When temperature is raised by $3 0^{\circ} C$ , then which of the following statement is correct?

Its density decreases.

Its density increases.

Its fractional decrease in density is $2.5 \times 1 0^{- 2}$ .

Its fractional increase in density is $2.5 \times 1 0^{- 2}$ .

Q. The coefficient of volume expansion of a liquid is 49×10−5K−1. When temperature is raised by 30∘C, then which of the following statement is correct?

Its density decreases.

Its density increases.

Its fractional decrease in density is 2.5×10−2.

Its fractional increase in density is 2.5×10−2.

Q. The coefficient of volume expansion of a liquid is $49 \times 1 0^{- 5} K^{- 1}$ . When temperature is raised by $3 0^{\circ} C$ , then which of the following statement is correct?

Its fractional decrease in density is $2.5 \times 1 0^{- 2}$ .

Its fractional increase in density is $2.5 \times 1 0^{- 2}$ .