Thermodynamics question: 4. One mole of a diatomic ideal gas initially occupies

Question

Thermodynamics question:

4. One mole of a diatomic ideal gas initially occupies the volume v, = 2.2711 L at p: 10.000 bar and Ti 273.15 K. The gas expands reversibly and adiabatically, to double its volume to V2-4.5422 L a) Find the pressure and the temperature at the end of the adiabatic expansion, assuming that the vibrational and electronic contributions to the heat capacity are negligible. b) Find the work done by the gas during the adiabatic expansion. c Find the heat that must be supplied to the gas to raise its temperature to 273.15 K, after the adiabatic expansion is over. Cv (5/2) Nk (S/2) nR for the diatomic gas, under the assumptions in this problem.

Explanation / Answer

a) for this process there is a relation between pressure and volume

(Pf/Pi) = (Vi/Vf)y

y= heat capacity ratio (Cp/Cv=3/5=0.6)

f and i sunscript denote final and initial respectively

putting the values,

Pf = (Vi/Vf)y * Pi

= (2.2711/4.5422)0.6 * 10

=(0.5)0.6 * 10

= 6.59 bar

PfVf= nRTf

Tf= PfVf/nR

= 6.50*4.5422/1*0.0821

= 359.6K

b) work done = -2.5*PiVi*((Vf/Vi)1-y-1)

= -2.5* 9.86*2.2711* ((2)1-0.6-1)

=-17.88J

c) Q= dU+W

dU= nCvdT

= 1* 20.78* (359.6-273.15)

= 1796.4J

Q= 1796.4+ (-17.88)

=1778.5J

=

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.