Serway & Jewett — Temperature: Problem 36

(a) Take the definition of the coefficient of volume expansion to be \[\beta = \frac{1}{V} \left. \frac{dV}{dT} \right|_{P=\text{constant}} = \frac{1}{V} \frac{\partial V}{\partial T}\] Use the equation of state for an ideal gas to show that the coefficient of volume expansion for an ideal gas at constant pressure is given by \(\beta = 1/T\), where \(T\) is the absolute temperature. (b) What value does this expression predict for \(\beta\) at \(0^\circ\text{C}\)? State how this result compares with the experimental values for (c) helium and (d) air in Table 18.1. Note: These values are much larger than the coefficients of volume expansion for most liquids and solids.