
Two identical square rods of metal are welded end to end as shown in figure (1), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (2), the same amount of heat will flow through the rods in

A. 1 minute
B. 2 minute
C. 4 minute
D. 16 minute
Answer
161.4k+ views
Hint:The rate of heat flow is defined as the amount of heat that is transferred per unit of time in any material. It is usually measured in watts (or joules per second). To solve this problem, we compare the rate of heat flow when the length of the material will double and when the area of the material will double.
Formula used:
Heat flow rate is given as,
\[\dfrac{{dh}}{{dt}} = k \times A \times \left( {\dfrac{{dT}}{{dx}}} \right)\]
Where k is the thermal conductivity, A is the boundary surface area and \[\dfrac{{dT}}{{dx}}\] temperature gradient.
Complete step by step solution:
As we know that the heat flow rate is given as,
\[\dfrac{{dh}}{{dt}} = \dfrac{{k \times A \times \Delta t}}{l}\]
As for the figure (1), with double length, we have
\[\dfrac{{20}}{4} = \dfrac{{k \times A \times \Delta t}}{{2l}}\] ……1
for figure (2), with double length, we have
\[\dfrac{{20}}{t} = \dfrac{{k \times 2A \times \Delta t}}{l}\] …….2
Now dividing equations 1 and 2, we get
\[\dfrac{t}{4} = \dfrac{1}{4}\]
\[\therefore t = 4\]
Time, t = 4 minute
Therefore, the same amount of heat will flow through the rods in 4 minutes.
Hence option C is the correct answer.
Note: Heat transfer is the process in which there is the exchange of heat from a high-temperature body to a low-temperature body. As kinetic energy is the parameter included by the particles in the system. When the temperature of a system increases then the kinetic energy of the particle in that system will also increase.
Formula used:
Heat flow rate is given as,
\[\dfrac{{dh}}{{dt}} = k \times A \times \left( {\dfrac{{dT}}{{dx}}} \right)\]
Where k is the thermal conductivity, A is the boundary surface area and \[\dfrac{{dT}}{{dx}}\] temperature gradient.
Complete step by step solution:
As we know that the heat flow rate is given as,
\[\dfrac{{dh}}{{dt}} = \dfrac{{k \times A \times \Delta t}}{l}\]
As for the figure (1), with double length, we have
\[\dfrac{{20}}{4} = \dfrac{{k \times A \times \Delta t}}{{2l}}\] ……1
for figure (2), with double length, we have
\[\dfrac{{20}}{t} = \dfrac{{k \times 2A \times \Delta t}}{l}\] …….2
Now dividing equations 1 and 2, we get
\[\dfrac{t}{4} = \dfrac{1}{4}\]
\[\therefore t = 4\]
Time, t = 4 minute
Therefore, the same amount of heat will flow through the rods in 4 minutes.
Hence option C is the correct answer.
Note: Heat transfer is the process in which there is the exchange of heat from a high-temperature body to a low-temperature body. As kinetic energy is the parameter included by the particles in the system. When the temperature of a system increases then the kinetic energy of the particle in that system will also increase.
Recently Updated Pages
A steel rail of length 5m and area of cross section class 11 physics JEE_Main

At which height is gravity zero class 11 physics JEE_Main

A nucleus of mass m + Delta m is at rest and decays class 11 physics JEE_MAIN

A wave is travelling along a string At an instant the class 11 physics JEE_Main

The length of a conductor is halved its conductivity class 11 physics JEE_Main

Two billiard balls of the same size and mass are in class 11 physics JEE_Main

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

JEE Main 2025: Derivation of Equation of Trajectory in Physics

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

Displacement-Time Graph and Velocity-Time Graph for JEE

Class 11 JEE Main Physics Mock Test 2025

Differentiate between audible and inaudible sounds class 11 physics JEE_Main

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

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

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

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

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