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5.1 Equal volumes of ideal gases at equal temperatures and total pressure contain equal numbers of molecules. Using the additional fact that one mole of a gas at STP will occupy 22.4 liters, determine the universal gas constant for an ideal gas in units of (a) atm-liters/gmole-K; (b) ft·lbflbmole-PR; (c) Btu/lbmole-"R; and (d) N.m/kgmole-K. 5.2 Calculate the mean free path for the gases found in Table 8.1 at (a) 298K and 10- atm pressure; (b) 298K and 0.1-atm pressure; and (c) 1,800K and l-atm pressure. 5.3 Consider 1 ft of air at STP. Determine (a) the acoustic velocity, ft/ sec; (b) the most probable speed, ft/sec; and (e) the mean square speed, ft/sec. Repeat parts (a)- (c) for T = 900°R. 5.4 Plot the speed distribution function Y as a function of molecular velocity V for helium at (a) 0°C; (6) 300°C; and (e) 900°C. From your results, show that by increasing temperature, the distribution will become broader, yielding more atoms having higher velocities and, hence, greater molecular energy. 5.5 A 0.5-m tank contains N, at 101 kPa and 298K. Calculate (a) the molecular density, molecules/cc; (b) the root mean square velocity, cm/sec; and (c) the mean molecular kinetic energy, N-m/molecule.