The coefficient of volume expansion of liquid is γ. The fractional change in its density for Δ T rise in temperature is

Question

The coefficient of volume expansion of liquid is &gamma;. The fractional change in its density for Δ T rise in temperature is (A) &gamma;Δ T (B) (Δ T/&gamma;) (C) 1+&gamma;Δ T (D) 1-&gamma;Δ T

Tardigrade Admin · Accepted Answer

On thermal expansion,
Volumetric expansion is given by

< b r / > V = V_{0} (1 + γ Δ T) \dots\dots (1) < b r / >

We know that, density,

d = \frac{mass}{volume}

d = \frac{m}{V}

where,

m =

constant

d \propto \frac{1}{V}

Density of the liquid varies as

< b r / > < b r / > d = d_{0} (1 + γ Δ T) < b r / > d = d_{0} + d_{0} γ Δ T < b r / > < b r / >

Fractional change in density is

< b r / > < b r / > \frac{d - d _{0}}{d _{0}} = γ Δ T < b r / > \frac{Δ d}{d _{0}} = γ Δ T < b r / > < b r / >

Q. The coefficient of volume expansion of liquid is $γ$ . The fractional change in its density for $Δ T$ rise in temperature is

$γ Δ T$

$\frac{Δ T}{γ}$

$1 + γ Δ T$

$1 - γ Δ T$

Q. The coefficient of volume expansion of liquid is γ. The fractional change in its density for ΔT rise in temperature is

γΔT

γΔT​

1+γΔT

1−γΔT

Q. The coefficient of volume expansion of liquid is $γ$ . The fractional change in its density for $Δ T$ rise in temperature is

$γ Δ T$

$\frac{Δ T}{γ}$

$1 + γ Δ T$

$1 - γ Δ T$