In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a U-tube connected the gas at one end. When the bulb is placed at the room temperature 27.0°C, the mercury column in the arm open to atmosphere stands 5.00 cm above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0 cm. Calculate the temperature of the liquid. (atmospheric pressure = 75.0 cm of mercury.)
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Question

In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a U-tube connected the gas at one end. When the bulb is placed at the room temperature 27.0°C, the mercury column in the arm open to atmosphere stands 5.00 cm above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0 cm. Calculate the temperature of the liquid. (atmospheric pressure = 75.0 cm of mercury.)

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G1 Physics · Accepted Answer

Use PV=nRT, U=(f/2)nRT, γ=1+2/f and vᵣₘₛ=√(3RT/M). At the same temperature, average translational kinetic energy depends only on T. Evaluating the given data/statements gives B: 177°C. Therefore the correct answer is B.