A cylindrical container is sealed with a movable piston and contains 0.200 mol o

Question

A cylindrical container is sealed with a movable piston and contains 0.200 mol of oxygen. The initial volume is 2.3.10-3 m3. and the initial temperature is 77°C. The value of the ideal gas constant is R = 8.315J/mol . K The oxygen, which can be approximated as an ideal gas, first undergoes an isochoric expansion to twice its original pressure. It is then expanded isothermally back to its original pressure. Finally, it is cooled isobarically to its original volume. 2.a) Give a definition of isobaric, isothermal, and isochoric transformations. Show the series of processes on a p-V diagram. Label your diagram clearly. [2] 2.b) Compute the temperature during the isothermal compression. [1] 2.c) Compute the maximum volume. [1] 2.d) Compute the total work done by the piston on the gas during the series of processes. [3] 2e) Compute the oxygen's internal energy change during the final isobaric compression. Use CP = 29.17 J/mol K. [2] 2.f) Compute the oxygen's internal energy change during the isothermal expansion. [1]

Explanation / Answer

2 a)

isobaric transformation : The kind of transformation during which the pressure remains constant

isothermal transformation : The kind of transformation during which no excahnge of heat takes place with the surrounding.

isochoric transformation : The kind of transformation during which the Volume remains constant

2 b)

isochoric expansion :

n = number of moles = 0.2 mol

Vi = initial Volume = 2.3 x 10-3 m3

Ti = initial temperature = 77 C = 77 + 273 = 350 K

Pi = initial pressure = ?

Using the equation

Pi Vi = n R Ti

Pi (2.3 x 10-3) = (0.2) (8.314) (350)

Pi = 2.53 x 105 Pa

Pf = 2 Pi = 2 (2.53 x 105 ) = 5.06 x 105 Pa

Pf/Pi = Tf/Ti

using the equation

2 = Tf/350

Tf = 700 K

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