
Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 minutes and 40 minutes respectively. Find the ratio of thermal conductivities of the materials.
A. 5:6
B. 6:5
C. 3:1
D. 2:1
Answer
164.1k+ views
Hint:In order to solve this problem we need to understand the thermal conductivity. The rate at which heat is transferred by conduction through a unit cross-section area of a material is known as thermal conductivity.
Formula Used:
To find the thermal conductivity the formula is,
\[\dfrac{Q}{t} = KA\dfrac{{\Delta T}}{L}\]
Where, A is a cross-sectional area, \[\Delta T\] is the temperature difference between two ends and L is the length of the cylinder.
Complete step by step solution:
The two vessels of different materials are similar in size in every respect means the area and length are the same. We need to find the ratio of thermal conductivity. It says the same quantity of ice gets melted, that is here Q and \[\Delta T\] remains the same. That is,
\[K \propto \dfrac{1}{t}\]
\[\Rightarrow \dfrac{{{K_1}}}{{{K_2}}} = \dfrac{{{t_2}}}{{{t_1}}}\]
Substitute the value of \[{t_1} = 20\min \] and \[{t_2} = 40\min \]we get,
\[\dfrac{{{K_1}}}{{{K_2}}} = \dfrac{{40}}{{20}}\]
\[\therefore \dfrac{{{K_1}}}{{{K_2}}} = \dfrac{2}{1}\]
That is, \[{K_1}:{K_2} = 2:1\]
Therefore, the ratio of thermal conductivities of the materials is 2:1.
Hence, option D is the correct answer.
Note:The reciprocal of thermal conductivity is known as thermal resistivity. The materials which have a high thermal conductivity are used in heat sinks whereas materials with low values are used as thermal insulators. In order to measure thermal conductivities of materials there exist several methods, which are broadly classified into two types of techniques one is transient and other is steady-state techniques.
Formula Used:
To find the thermal conductivity the formula is,
\[\dfrac{Q}{t} = KA\dfrac{{\Delta T}}{L}\]
Where, A is a cross-sectional area, \[\Delta T\] is the temperature difference between two ends and L is the length of the cylinder.
Complete step by step solution:
The two vessels of different materials are similar in size in every respect means the area and length are the same. We need to find the ratio of thermal conductivity. It says the same quantity of ice gets melted, that is here Q and \[\Delta T\] remains the same. That is,
\[K \propto \dfrac{1}{t}\]
\[\Rightarrow \dfrac{{{K_1}}}{{{K_2}}} = \dfrac{{{t_2}}}{{{t_1}}}\]
Substitute the value of \[{t_1} = 20\min \] and \[{t_2} = 40\min \]we get,
\[\dfrac{{{K_1}}}{{{K_2}}} = \dfrac{{40}}{{20}}\]
\[\therefore \dfrac{{{K_1}}}{{{K_2}}} = \dfrac{2}{1}\]
That is, \[{K_1}:{K_2} = 2:1\]
Therefore, the ratio of thermal conductivities of the materials is 2:1.
Hence, option D is the correct answer.
Note:The reciprocal of thermal conductivity is known as thermal resistivity. The materials which have a high thermal conductivity are used in heat sinks whereas materials with low values are used as thermal insulators. In order to measure thermal conductivities of materials there exist several methods, which are broadly classified into two types of techniques one is transient and other is steady-state techniques.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
