If d1 and d2 are the densities of a liquid at t1 ° C and t1 ° C then (d1/d2) is (g = coefficient of real expansion)

Question

If d1 and d2 are the densities of a liquid at t1 ° C and t1 ° C then (d1/d2) is (g = coefficient of real expansion) (A) (1+&gamma; t1/1+&gamma; t2) (B) (1-&gamma; t1/1-&gamma; t2) (C) (1+&gamma; t2/1+&gamma; t1) (D) (1-&gamma; t2/1-&gamma; t1)

Tardigrade Admin · Accepted Answer

Let the density of liquid at 0° C be d 0. Longrightarrow d 1=( d 0/1+&gamma; t 1) Also d 2=( d 0/1+&gamma; t 2) Longrightarrow ( d 1/ d 2)=(1+&gamma; t 2/1+&gamma; t 1)

Q. If $d_{1}$ and $d_{2}$ are the densities of a liquid at $t_{1}^{\circ} C$ and $t_{1}^{\circ} C$ then $\frac{d _{1}}{d _{2}}$ is (g = coefficient of real expansion)

$\frac{1 + γ t _{1}}{1 + γ t _{2}}$

$\frac{1 - γ t _{1}}{1 - γ t _{2}}$

$\frac{1 + γ t _{2}}{1 + γ t _{1}}$

$\frac{1 - γ t _{2}}{1 - γ t _{1}}$

Let the density of liquid at $0^{\circ} C$ be $d_{0}$ .
$< b r / >⟹ d_{1} = \frac{d _{0}}{1 + γ t _{1}} < b r / >$
Also $d_{2} = \frac{d _{0}}{1 + γ t _{2}}$
$< b r / >⟹ \frac{d _{1}}{d _{2}} = \frac{1 + γ t _{2}}{1 + γ t _{1}} < b r / >$

Q. If d1​ and d2​ are the densities of a liquid at t1​∘C and t1​∘C then d2​d1​​ is (g = coefficient of real expansion)

1+γt2​1+γt1​​

1−γt2​1−γt1​​

1+γt1​1+γt2​​

1−γt1​1−γt2​​