An experiment is performed to determine the number n of moles of an ideal gas in the cylinder shown above. The cylinder is fitted with a movable, frictionless piston of area A. The piston is in equilibrium and is supported by the pressure of the gas. The gas is heated while its pressure P remains constant. Measurements are made of the temperature T of the gas and the height H of the bottom of the piston above the base of the cylinder and are recorded in the table below. Assume that the thermal expansion of the apparatus can be ignored.
T (K) H (m)
300 1.11
325 1.19
355 1.29
375 1.37
405 1.47
a) Write a relationship between the quantities T and H, in terms of the given quantities and fundamental constants, that will allow you to determine n.
b) Plot the data on the axes below so that you will be able to determine n from the relationship in part (a). Label the axes with appropriate numbers to show the scale
c) Using your graph and the values A = 0.027 m2 and P = 1.0 atmosphere, determine the experimental value of n.
