In a separate investigation

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

In a separate investigation, a research team seals a precisely known mass of helium gas inside a rigid vessel of volume

2.50 \times 10^{-3}\;\text{m}^{3}

. The sealed vessel is equipped with a precision pressure gauge and a thermistor thermometer. The mass of the helium is

0.200\;\text{g}

, and the molar mass of helium is

4.00\;\text{g}\,\text{mol}^{-1}

. During the measurement the gauge reads

1.00 \times 10^{5}\;\text{Pa}

while the thermometer indicates

310\;\text{K}

. Assume helium behaves ideally. Avogadro’s number is

N_{A}=6.022\times10^{23}\;\text{mol}^{-1}

. (1) Calculate the total number of helium atoms

N

contained in the vessel. (2) Using the measured pressure, temperature, and volume together with the value of

N

, determine the Boltzmann constant

k_{B}

. (3) From your value of

k_{B}

, compute a corresponding value of the universal gas constant

R

. (4) The accepted values are

k_{B}=1.38\times10^{-23}\;\text{J}\,\text{K}^{-1}

and

R = 8.314\;\text{J}\,\text{mol}^{-1}\,\text{K}^{-1}

. Calculate the percent difference between your experimental constants and the accepted values. Discuss at least two experimental factors that could account for the observed differences, specifying whether each factor would tend to raise or lower the calculated constants.

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