Question

A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and
temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and
internal energy, respectively. The correct option(s) is (are)
(A) qᴀᴄ = △Uвᴄ and wᴀв = P2(V2—V1) (B) Wвᴄ = P2(V2—V1) and qвᴄ = △Hᴀᴄ
(C) △Hᴄᴀ < △Uᴄᴀ and qᴀᴄ = △Uвᴄ (D) qвᴄ = △Hᴀᴄ and △Hᴄᴀ > △Uᴄᴀ

Answer 1

Question:

A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively. The correct option(s) is (are)

(A) qᴀᴄ = △Uвᴄ and wᴀв = P2(V2—V1) (B) Wвᴄ = P2(V2—V1) and qвᴄ = △Hᴀᴄ

(C) △Hᴄᴀ < △Uᴄᴀ and qᴀᴄ = △Uвᴄ (D) qвᴄ = △Hᴀᴄ and △Hᴄᴀ > △Uᴄᴀ

Solution:

From the figure given above we can identify,

AC = isochoric process

AB = isothermal process

BC = isobaric process

qAC = ΔUAC = nCv,m(T2 – T1) = ΔUBC

W_AB = -nRT1 ln(V2 / V1)

WBC = –P2(V1 – V2) = P2(V2 – V1)

⇒ qBC = ΔHBC = nCP,m(T2 – T1) = ΔHAC

ΔHCA = nCP,m(T1 – T2)

⇒ ΔUCA = nCV,m(T1 – T2)

So, ΔHCA < ΔUCA since both are negative (T1 < T2)

Hence option C is correct.