SATHEE: Properties Of Solids And Liquids Question 559

Properties Of Solids And Liquids Question 559

Question: DIRECTION: Read the passage given below and answer the questions that follows:

In a thermally insulated tube of cross sectional area $\frac{G M m}{2 R}$ a liquid of thermal expansion coefficient $10^{- 3} K^{- 1}$ is flowing. Its velocity at the entrance is $0.1 m / s$ . At the middle of the tube a heater of a power of 10kW is heating the liquid. The specific heat capacity of the liquid is 1.5 kJ/(kg K), and its density is $1500 k g / m^{3}$ at the entrance. The rise in temperature of the liquid as it pass through the tube is

Options:

A) $\frac{1000}{9}^{\circ} C$

B) $\frac{1}{9}^{\circ} C$

C) $\frac{500}{9}^{\circ} C$

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

$ρ_{1} v_{1} A_{1} = ρ_{2} v_{2} A_{2}$

$m =1500 kg/ m^{3} \times 0 .1m/s \times 4 {(cm)}^{2}$

$m s Δ T = 10000$

$1500 \times 0.1 \times 4 \times 10^{- 4} \times 1500 \times Δ T = 10000$

$Δ T = \frac{10000}{90} = \frac{1000}{9}^{\circ} C$

$ρ_{2} = \frac{ρ_{1}}{(1 + γ Δ T)} = \frac{1500}{(1 + 1 \times 10^{3} \times \frac{1000}{9})} = 1350 k g / m^{3}$

$ρ_{2} v_{2} A_{2} = ρ_{1} v_{1} A_{1}$

$\Rightarrow 1350 \times v_{2} = 1500 \times 0.1$

$v_{2} = 1 / 9 m / s$

$∴$ Volume rate of flow at the end of tube

$= A_{2} v_{2} = 4 \times 10^{- 4} \times \frac{1}{9}$

$= \frac{4}{9} \times 10^{- 4} m^{3} = \frac{40}{9} \times 10^{- 5} m^{3}$

Volume rate of flow at the entrance = $A_{1} v_{1}$

$= 0.1 \times 4 \times 10^{- 4} = 4 \times 10^{- 5} m^{3}$

Hence, difference of volume rate of flow at the two ends

$= (\frac{40}{9} - 4) \times 10^{- 5} = \frac{4}{9} \times 10^{- 5} m^{3}$

Properties Of Solids And Liquids Question 559

Question: DIRECTION: Read the passage given below and answer the questions that follows:

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Properties Of Solids And Liquids Question 559

Question: DIRECTION: Read the passage given below and answer the questions that follows:

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu