Question

The coefficient of volume expansion of glycerine is 49 × 10⁻⁵ K⁻¹. What is the fractional change in its density for 30° C rise in temperature?

Answer 1

Coefficient of volume expansion of glycerin, αV = 49 × 10–5 K–1

Rise in temperature, ΔT = 30°C

Fractional change in its volume =

This change is related with the change in temperature as:




Where,

m = Mass of glycerine

px= Initial density at T1

qx= Final density at T2


Where,

px.qx= Fractional change in density

∴Fractional change in the density of glycerin = 49 ×10–5 × 30 = 1.47 × 10–2

Answer 2

Answer:

• $1.47 \times 10^{-2}$

Explanation:

• Coefficient of volume expansion of glycerin, $\alpha_{V}= 9\times 10^{-5}K^{-1}$
• Rise in temperature, $\Delta T = 30^{o}C$
• Fractional change in its volume = $\frac{\Delta V}{V}$

This change is related to the change in temperature as:

$\dfrac{ \Delta V }{V}= \alpha_{V} \Delta T$

$V_{T_{2}}-V_{T_{1}}= V_{T_{1}} \alpha_{V} \Delta T$

$\frac{m}{\rho _{T_{2}}}-\frac{m}{\rho_{T_{1}}} = \frac{m}{\rho_{T_{1}}}\alpha_{V}\Delta T$

Where,

• m = Mass of glycerine
• $\rho_{T_{1}}$ = Initial density at $T_{1}$
• $\rho_{T_{2}}$ = Final density at $T_{2}$

$\frac{\rho_{T_{1}} - \rho_{T_{2}}}{ \rho_{T_{2}}} = \alpha_{V}\Delta T$

Where,

• $\frac{\rho_{T_{1}} - \rho_{T_{2}}}{ \rho_{T_{2}}}$ = Fractional change in density

Fractional change in the density of glycerin:

$\implies\:\:\:49\times 10^{-5} \times 30 = 1.47 \times 10^{-2}$