SATHEE: Heat and Thermodynamics 3 Question 13

Heat and Thermodynamics 3 Question 13

13. Two identical conducting rods are first connected independently to two vessels, one containing water at $100^{\circ} C$ and the other containing ice at $0^{\circ} C$ . In the second case, the rods are joined end to end and connected to the same vessels. Let $q_{1}$ and $q_{2}$ gram per second be the rate of melting of ice in the two cases respectively. The ratio $\frac{q_{1}}{q_{2}}$ is

(2004, 2M)

(a) $\frac{1}{2}$

(b) $\frac{2}{1}$

(d) $\frac{1}{4}$

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Answer:

Correct Answer: 13. (c)

Solution:

$\frac{d Q}{d t} = L (\frac{d m}{d t})$

or $\frac{Temperature difference}{Thermal resistance} = L (\frac{d m}{d t})$

$\begin{aligned} or & \frac{d m}{d t} & \propto \frac{1}{Thermal resistance} \\ \Rightarrow & q & \propto \frac{1}{R} \end{aligned}$

In the first case rods are in parallel and thermal resistance is $\frac{R}{2}$ while in second case rods are in series and thermal resistance is $2 R$ .

$\frac{q_{1}}{q_{2}} = \frac{2 R}{R / 2} = \frac{4}{1}$

Heat and Thermodynamics 3 Question 13

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Heat and Thermodynamics 3 Question 13

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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