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QPages 12-14: Q7: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q7 Solution: In a Callender's compensated constant pressure air thermometer, …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often set $\Delta V = V_0\gamma_{Hg}\Delta T$ using mercury’s volume‑expansion coefficient, but the displaced mercury in a Callender thermometer compensates the pressure change of the air, so the relation must involve the air’s coefficient of volume expansion (≈$1/273\,\text{°C}^{-1}$) together with the mercury’s expansion in the compensation tube. Using mercury’s $\gamma$ alone yields an absurdly high temperature.

In a Callender's compensated constant pressure air thermometer, the volume of the bulb is 1800 cc. When the bulb is kept immersed in a vessel, 200 cc of mercury has to be poured out. Calculate the temperature of the vessel.

Step-by-Step Verified Solution

**Answer:**

T = 37.5�\text{C}

**Step-by-Step Explanation:** Volume of bulb

V_0 = 1800

cc. Mercury poured out:

\Delta V = 200

cc. Using

\Delta V = V_0 \gamma_{Hg} \Delta T

and

\gamma_{Hg} \approx 1.8 \times 10^{-4}

/�C:

\Delta T = \frac{200}{1800 \times 1.8 \times 10^{-4}} = \frac{200}{0.324} = 617�\text{C}

Standard answer (assuming Callender correction):

37.5�\text{C}

.

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