# (1) A cylinder enclosed by a piston of negligible by fmx14915

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```									(1) A cylinder enclosed by a piston of negligible mass is sitting on a lab bench at 25°C. The
cylinder contains 0.15 moles of helium gas, which is initially in thermodynamic equilibrium
with its surroundings. The piston is initially at a height of 8 cm above the bottom of the
cylinder. A series of small weights are gradually added to the top of the piston, and the
piston moves downwards to a height of 5 cm above the bottom of the cylinder. The radius
of the cylinder is 4 cm. Find the total mass, M, of the small weights if the process is (a)
isothermal and (b) adiabatic.

(2) 1.5 moles of an ideal gas initially at 20°C and 1.00 x 106 Pa undergoes a two-step process.
The molar specific heat at constant volume for this gas is 3R/2. For each of the two steps
described below, calculate the final pressure, as well as q, w, !U, and !H.

(a) Step 1: Reversible isothermal expansion until the volume of the gas doubles.

(b) Step 2: The temperature is increased to 80°C at a constant volume.

(c) What is the total heat transferred to the system as a result of this overall two-step
process?

(3) One mole of air at 1 bar and 25 oC is compressed to 5 bar and 25 oC by two different
mechanically reversible processes:

(a) Cooling at constant pressure followed by heating at constant volume

(b) Heating at constant volume followed by cooling at constant pressure

Calculate q, w, !U, and !H of the air for each path. Heat capacities of the air (which is
independent of the temperature) are Cv = 20.78, and Cp = 29. 10 Jmol-1K-1. Assume PV/T is
constant, regardless of the change it undergoes. At 25 oC and 1 bar the molar volume of air
is 0.02479 m3 mol-1.

(4) One mole of an ideal gas undergoes the following sequence of mechanically reversible
process in a closed system:

(a) From an initial state of 70 oC and 1 bar, it is compressed adiabatically to 150 oC.

(b) it is then cooled from 150 to 70 oC at constant pressure

(c) Finally, it is expanded isothermally to its original state

Calculate w, q, !U, !H for each of the three process and for the entire cycle. Draw the PV
diagram for the entire cycle and label them. Consider Cv as 3/2R

(5) One mole of liquid water at 100OC is heated until the liquid is converted entirely to vapor at
100OC and 1 atm pressure. Calculate q, w, !U, and !H for each of the following. Heat of
condensation is -40.66 kJ/mol. The density of liquid water at 20OC and 100OC are 998.21
kg/m3 and 958.4 kg/m3, respectively. The density of water vapor at 20OC and 100OC are
0.5968 kg/m3 and 0.7580 kg/m3, respectively
(a)   The vaporization is carried out in a cylinder where the external pressure on the
piston is maintained at 1atm throughout.
(b)   The cylinder is first expanded against a vacuum to the same volume as in part
(a) and then sufficient heat is added to vaporize the the liquid completely to 1atm
pressure

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