A steel cylinder with rigid walls is evacuated to a high degree of vacuum; you then put a small amount of helium into the cylinder. The cylinder has a pressure gauge that measures the pressure of the gas inside the cylinder. You place the cylinder in various temperature environments, wait for thermal equilibrium to be established, and then measure the pressure of the gas. You obtain these results:

(a) Recall (Chapter 17) that absolute zero is the temperature at which the pressure of an ideal gas becomes zero. Use the data in the table to calculate the value of absolute zero in °C. Assume that the pressure of the gas is low enough for it to be treated as an ideal gas, and ignore the change in volume of the cylinder as its temperature is changed.

(b) Use the coefficient of volume expansion for steel in Table 17.2 to calculate the percentage change in the volume of the cylinder between the lowest and highest temperatures in the table. Is it accurate to ignore the volume change of the cylinder as the temperature changes? Justify your answer.

Table 17.2

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P (Pa) T(°C) -195.8 0.0 33.3 100.0 Normal boiling point of nitrogen Ice-water mixture Outdoors on a warm day Normal boiling point of water Hot oven 254 890 999 1214 1635 232 Coefficients of Volume Expansion Solids В (к- оr (С)-1] Liquids B [K-! or (C°)-'] 75 x 10-5 115 x 10-5 Aluminum 7.2 x 10-5 Ethanol Brass 6.0 x 10-5 Carbon disulfide Copper 5.1 x 10-5 Glycerin 49 x 10-5 Glass 1.2-2.7 x 10-5 Mercury 18 x 10-5 Invar 0.27 x 10-5 Quartz (fused) 0.12 x 10-5 Steel 3.6 x 10-5