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(a)
When 117 J of energy is supplied as heat to 2.00 moles of an idealgas at constant
pressure, the temperature rises by 2.00 K. Calculate the molar heatcapacity at constant
pressure, CP,m and the molar heat capacity at constant volume, CV,mfor the gas. By
considering the two heat capacities, determine whether the gas ismonatomic or diatomic.

(b)

Explain what isothermal processes and adiabatic processes are,and the differences
between them, taking care to explain the role, or otherwise, of theenvironment to which the
system under study is exposed.

(c)

A sample of 8.02 × 10−1 moles of nitrogen gas (with γ = 1.40)occupies a volume of
2.00 × 10−2m3 at a pressure of 1.00 × 105 Pa and a temperature of300K. The sample is
adiabatically compressed to exactly half its original volume.Nitrogen behaves as an ideal gas
under these conditions.

(i) What is the change in entropy of the gas?
(ii) Show from the adiabatic condition and the equation of statethat TV (γ−1) remains
constant, and hence determine the final temperature of the gas.

(d) The gas sample is now returned to its initial state and thenisothermally compressed to
half its original volume.
(i) Find the change in entropy of the gas.
(ii) What is the change in internal energy of the gas?
(iii) What is the amount of heat transferred from the gas to itsenvironment?
(iv) Calculate the amount of work done in compressing the gas.