SATHEE: Thermal Properties of Matter

Thermal Properties of Matter - Result Question 3

3. The value of coefficient of volume expansion of glycerine is $5 \times 10^{- 4} K^{- 1}$ . The fractional change in the density of glycerine for a rise of $40^{\circ} C$ in its temperature, is:

[2015 RS]

(a) 0.020

(b) 0.025

(d) 0.015

Show Answer

Answer:

Correct Answer: 3. (a)

Solution:

(a) From question,

Rise in temperature $Δ t = 40^{\circ} C$

Coefficient of volume expansion

$γ = 5 \times 10^{- 4} K^{- 1}$

Fractional change in the density $\frac{Δ ρ}{ρ_{0}} = \frac{ρ_{0} - ρ_{T}}{ρ_{0}}$

$ρ_{T} = ρ_{0} (1 - γ Δ t)$

$\Rightarrow \frac{Δ ρ}{ρ_{0}} = \frac{ρ_{0} - ρ_{T}}{ρ_{0}} = γ Δ T = (5 \times 10^{- 4}) (40) = 0.020$

Most substances (solid & liquid) expand when they are heated, so volume of a given mass of a substance increases on heating so density decreases as

$\begin{aligned} ρ \propto \frac{1}{V} \Rightarrow \frac{ρ^{'}}{ρ} = \frac{V}{V^{'}} = \frac{V}{V + Δ V} \\ = \frac{V}{V + γ V A θ} = \frac{1}{1 + γ Δ θ} \end{aligned}$

Thermal Properties of Matter - Result Question 3

3. The value of coefficient of volume expansion of glycerine is $5 \times 10^{- 4} K^{- 1}$ . The fractional change in the density of glycerine for a rise of $40^{\circ} C$ in its temperature, is:

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Thermal Properties of Matter - Result Question 3

3. The value of coefficient of volume expansion of glycerine is 5×10−4K−1. The fractional change in the density of glycerine for a rise of 40∘C in its temperature, is:

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

3. The value of coefficient of volume expansion of glycerine is $5 \times 10^{- 4} K^{- 1}$ . The fractional change in the density of glycerine for a rise of $40^{\circ} C$ in its temperature, is: