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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Heat and Temperature

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Heat and Temperature

A glass vessel has a volume of 1000 cc at 20^ ^ ^ C . Determine the...

A glass vessel has a volume of 1000 cc1000 \text{ cc} at 20^{}^{{}^{\circ}} C. Determine the volume of mercury that must be poured into the vessel at this temperature to ensure that the volume of the remaining space remains constant as the temperature varies. The coefficients of cubical expansion for mercury and glass are 1.8 \times 10^{-4} ^{}^{{}^{\circ}} C^{-1} and 9.0 \times 10^{-6} ^{}^{{}^{\circ}} C^{-1}, respectively.

Options

  1. A150 cc150 \text{ cc}
  2. B100 cc100 \text{ cc}
  3. C50 cc50 \text{ cc}
  4. D200 cc200 \text{ cc}

Correct answer

C. 50 cc50 \text{ cc}

Step-by-step solution

Let VgV_g be the volume of the glass vessel and VmV_m be the volume of mercury.

The volume of the empty space is Vg−VmV_g - V_m. For this volume to remain constant with temperature, the change in volume of the glass vessel must be equal to the change in volume of the mercury.

ΔVg=ΔVm\Delta V_g = \Delta V_m

VgγgΔT=VmγmΔTV_g \gamma_g \Delta T = V_m \gamma_m \Delta T

Vm=VgγgγmV_m = V_g \dfrac{\gamma_g}{\gamma_m}

Substituting the given values:

Vm=1000×9.0×10−61.8×10−4V_m = 1000 \times \dfrac{9.0 \times 10^{-6}}{1.8 \times 10^{-4}}

Vm=1000×9180V_m = 1000 \times \dfrac{9}{180}

Vm=1000×120V_m = 1000 \times \dfrac{1}{20}

Vm=50 ccV_m = 50 \text{ cc}
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