calculate the work done when an ideal gas expands isothermally and reversibly in

Question

calculate the work done when an ideal gas expands isothermally and reversibly in a piston and cylinder assembly

knowing that SW= pdv and for ideal gas P= PT/V where V is the volume

for expansion of a gas at 300k from an initial pressure bar to final pressure 1 bar

Explanation / Answer

(i) Use Tds equation, Tds = du + pdv, integrate from T2 to T1 ?S = n ?s = n Cv ln T2/T1 + R ln V2/V1, T2 = T1 ?S = nR ln V2/V1 = 5 [mol]*8.314 [J/mol K] ln 168/112 = 16.855 J/K (ii) Wsys = ?pdv, p1v1 = p2v2 = k --> p = k/v Wsys = ?K/V dV = k ? 1/v dv, Integrate from v1 to v2 Wsys = k (ln v2/v1) = RT ln v2/v1 = T*?S = 273*16.855 =4601.465 J = 4.601 kJ (work done on the system) (iii) Closed system energy balance ?U = Q - W = mC?T= 0 = Q-W Q = W = T?S = W (reversible) = 4.601 kJ (from the surroundings) (iv) ?S surr = -?S system = - 16.855 J/K (v) ?S total = ?S surr + ?S system = - 16.855 + 16.855 = 0

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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