2 (15%) Consider a tapered bar of circular cross section. The length of the bar is 1m, and the radius varies as r(x)= 0.05–0.04x, where r and x are in

2.51 A tank contains 20 L of compressed nitrogen at 10 bar and 25 °C. Calculate the maximum work that can be obtained when the gas is allowed to expand reversibly to 1 bar pressure(a) isothermally and (b) adiabatically. The heat capacity of nitrogen at constant volume can be taken to be 20.8 J K mol^-1 independent of temperature.

Problem 3.33 Within a cubic unit cell, sketch the following directions: Required problems are a, d, and g. The remaining problems are optional but are provided for addedpractice. Solutions will be provided for all of these problems.

ESCIb) The following temperature/composition data were obtained for a mixture of two liquids A and B at 1,00 atm, where x is the mole fraction in the liquid and y the mole fraction in the vapour at equilibrium.

1.14 The isothermal compressibility K of a gas is defined in Problem 1.17, and its value for an ideal gas is shown to be 1/P.Use implicit differentiation of V with respect to P at constant T to obtain the expression for the isothermal compressibility of a van der Waals gas. Show that in the limit of infinite volume, the value for an ideal gas is obtained.

4-66 5 kg of Argon is compressed in a polytropic process with n = 1.2 from 120 kPa and 108"C to 800 kPa in a piston-cylinder device. Determine the work produced and heat transferred during this compression process.

ESAI(a) A water carbonating plant is available for use in the home and operates by providing carbon dioxide at 5.0 atm. Estimate the molar concentration of CO, in the carbonated water it produces.

ESC.1la) The following temperature-composition data were obtained for a mixture of octane (O) and methylbenzene (M) at 1.00 atm, where x is the mole fraction in the liquid and y the mole fraction in the vapour at equilibrium. The boiling points are 110.6°C and 125.6 °C for M and O, respectively. Plot the temperature-composition diagram for the mixture. What is the composition of the vapour in equilibrium with the liquid of composition (i) x,, = 0.250 and(ii) x, = 0.250?

1.6 Show how the second virial coefficient of a gas and its molar mass can be obtained by plotting P/p versus P, where p is the density of the gas. Apply this method to the following data on ethane at 300 K. P/bar 1 10 20 p/10^-3 g cm^-3 1.2145 13.006 28.235

9.46 An atom makes a transition from an excited state with a lifetime of 10-9 s to the ground state and emits a photon with a wavelength 600 nm. What is the uncertainty in the energy of the excited state? What is the percentage uncertainty if the energy is measured from the ground state?

A detector is exposed to a monochromatic source of radiation for 40 ms and indicates that the power level is 10 µW.If 10° photons are incident on the detector in this time, what is the frequency of the radiation? What type of electromagnetic radiation is this?