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Question #42128

Difficulty: 8/10 | 🟢 Free

The Question

An ideal diatomic gas ( $\gamma = 1.4$ ) is initially at a temperature of $27^\circ\text{C}$ . It is compressed adiabatically to $\frac{1}{32}$ of its original volume. A faulty thermometer is used to measure the temperature of the gas. This thermometer exhibits a linear response, reading $10^\circ\text{X}$ at the melting point of ice and $160^\circ\text{X}$ at the boiling point of water at standard atmospheric pressure. What is the final temperature of the gas as measured by this faulty thermometer? (Assume $0^\circ\text{C} = 273\text{ K}$ )

Options

A.
$1400.5^\circ\text{X}$
B.
$1810.0^\circ\text{X}$
C.
$172.0^\circ\text{X}$
D.
$202.0^\circ\text{X}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Celsius-Fahrenheit Calibration Errors|Adiabatic/Isothermal Processes via KTG

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between absolute thermodynamic temperature and empirical temperature scales.

A common trap is applying the adiabatic equation $TV^{\gamma-1} = \text{constant}$ directly to Celsius or the faulty scale, which violates the derivation from the ideal gas law $PV=nRT$ (where $T$ must be in Kelvin).

Another frequent error is calculating the correct final Kelvin temperature but plugging it directly into the Celsius-based linear calibration mapping without subtracting 273, leading to the trap answer of $1810^\circ\text{X}$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermal Properties of Matter - Class 11 Part 2
Concept	Celsius-Fahrenheit Calibration Errors
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free