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Question #42147

Difficulty: 8/10 | 🟢 Free

The Question

A heating coil is submerged in a calorimeter containing a liquid. The coil is connected to a constant voltage source of $V = 20\ \text{V}$ . The resistance of the coil at the surrounding temperature $T_s = 25^\circ\text{C}$ is $R_0 = 10\ \Omega$ , and its temperature coefficient of resistance is $\alpha = 0.05\ ^\circ\text{C}^{-1}$ . The calorimeter loses heat to the surroundings according to Newton's law of cooling, with a heat transfer coefficient $k = 1\ \text{W/}^\circ\text{C}$ . Assuming the liquid is continuously stirred and maintains a uniform temperature, what is the steady-state temperature of the liquid?

Options

A.
$45^\circ\text{C}$
B.
$65^\circ\text{C}$
C.
$-15^\circ\text{C}$
D.
$55^\circ\text{C}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Calorimetry with Heat Loss|Internal Resistance Variation|Current Electricity

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to model a non-linear thermal-electric feedback loop.

A common trap is assuming the power dissipated by the coil remains constant ( $P = V^2/R_0$ ), which ignores the temperature dependence of the internal resistance.

By doing so, students incorrectly calculate a linear steady-state condition (yielding $65^\circ\text{C}$ ), failing to recognize that as the temperature rises, the resistance increases, thereby reducing the Joule heating rate and leading to a lower actual steady-state temperature.

Another trap is incorrectly using $P = I^2R$ while assuming constant current, which yields a physically absurd negative temperature change.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermal Properties of Matter - Class 11 Part 2
Concept	Calorimetry with Heat Loss
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free