Question

After a free expansion to increase its volume by a factor of six, a mole of ideal monatomic gas is compressed back to its original volume isobarically and then warmed up isochorically to its original temperature. What is the heat added to the gas in the final step to restoring its original state? (Use the following as necessary: p₀ for the initial pressure and V₀ for the initial volume.)

(The answer is not 7.5*p_0*v_0)

Answer 1

Here we apply definition of thermodynamics processes and first law of thermodynamics.

An first fort tree free expansion to sixth fold volume e = 60 no. of moles of gas, n=1 None' deobaric compression clush that = then ilochoric process such that 1 Iz = To Before freeexpansion, Volume = Vo Temperature = To In free expansion, gas expands «n Yaccим е р о — c. Work done W = o =o ay adiabatic process. so from first law of thermodynants Q = suth DAV=o tuin free ese parison so after free expansion pq / 2 1 2 Volume, v = Gvo - Temperature, I, eta Now isobaric Compression so Prest ure is constant I QV 6

6 Now in third step is ochoric process = constant To Work done, Wisoo Now final temperature, If = To Leo change in internal energy AU = ncuc Ts - Tz > JU=(0) LR (To-To) a Car su= FR TO Ideal gas equation р/ = neT - Po Vo=nRTO n=1 Povo = RTo o AU = s Povo from first law of thermodynamics T Q = AU TW » Q = s polo to gas in final To head added to Lastep as 5/4 Povo