[1] Obatin heat q and work w given to an ideal gas (1 mol) system and the change

Question

[1] Obatin heat q and work w given to an ideal gas (1 mol) system and the change of the internal energy U in the following processes. Heat capacity at constant volume, Cv, of the gas does depend on the temerpature.

1. Obtain heat q and work w given to an ideal gas (1 mo) system and the change of the internal energy U in the following processes. Heat capacity at constant volume, Cv, of the gas does not depend on temperature. a) A reversible isothermal expansion from (P1M,7,) to (Pg 7,). b) A reversible adiabatic expansion from (PM,7,) to (Py½,T2) and then heating the gas reversibly at constant volume from (Pvv. T2) to (Pe½). A reversible constant pressure expansion from (A, ½,7,) to (P1,½,%) and then cooling the gas reversibly at constant volume from (P1,½,T2) to (P2, ½,7,). c)

Explanation / Answer

1.for ideal gas, change in internal energy =0 and work done = n( no of moles)*RT1*ln(V1/V2), V1= initial volunme and V2= final volume, work done for one moles of gas = RT1*ln(V1/V2), deltU= Q+W or Q=-W= -RT1*ln(V1/V2)

2. for adiabatic expansion, Q=0 and from 1st law of thermodynamics, deltaU( change in internal energy)= Q( heat)+W( work)

or delaU= W for one moles of gas = R*(T2-T1)/(Y-1), Y= CP/CV= ratio of specific heats of gases

for constant volume process from P3,V3, T2 to P2,V2 and T1

deltaU= 1*CV*(T1-T2), work done = PdV= 0, deltaU= Q+W, Q= CV*(T2-T1)

3. the 1st step is constant pressure ( isobaric process) and for this process, work done = PdV= P1*(V2-V1) and delltaU= Cv*(T3-T1), deltaU= Q+W, Q= deltaU-W= CV*(T3-T1)-P1*(V2-V1)

cooling at constant volume, work done= 0 for ideal gas and deltaU= Cv*(T1-T3), deltaU= Q+W, Q= deltaU= Cv*(T1-T3)

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