question 5/5?

Question

1 moles of an ideal gas at T =313K is cooled down in an isovolumetric process and as a consequence the pressure drops for a factor of 2.1. After that the gas expands in an isobaric process till the initial temperature T is reached. Calculate the amount of heat (in kJ) absorbed by the gas during the whole process.

Answer 1

Please understand that the heat absorbed by the gas is for increasing the internal energy as well as doing work on the environment. From the beginning to the end of the whole process, the gas temperature is not changed, hence the contribution to the internal energy is zero. What we need to calculate is the work done by the system. During the first isovolumetric process, work is zero. During the second isobaric process, the work can be calculated as: p(Vf - Vi)
where p the final lower pressure, Vf and Vi the final and initial volumes, and P the initial high pressure.
p*Vf = RT = 313*8.314 (J), and p*Vi = (P/2.1)*Vi = (P*Vi)/2.1 = RT/2.1 = 313*8.314/2.1 (J). Thus the amount of heat absorbed by the gas during the whole process is:
p(Vf - Vi) = 313*8.314*(1-1/2.1) J = 1363 J = 1.36 kJ (answer)