Chemistry - Thermodynamics - I Question with Solution | TestHub
A cylinder with thermally insulated walls contains an insulated portion which can slide freely. The partition divides the cylinder into two chambers containing equal moles of the same gas, the initial pressure, temperature and volume being Po, To and Vo, respectively. By means of heating coil, heat is supplied slowly to the gas in one chamber until its pressure becomes 27Po/8. If the value of γ is 1.5, find the heat supplied to the gas in chamber A.
Options:
Answer:
Solution:
Chamber B (no heat) is compressed reversibly and adiabatically to Pf = 27Po/8: VB = Vo(8/27)2/3 = 4/9Vo, TB = To·27/8·4/9 = 1.5To. Chamber A has the same pressure and VA = 2Vo - 4/9Vo = 14/9Vo, so TA = To ·27/8·14/9 = 5.25To. With nR = PoVo/To and CV = R/(γ - 1) = 2R per mole: heat to A = Δ UA + Δ UB (B received only work from A) = 2(PoVo)/(To)[(5.25 - 1) + (1.5 - 1)]To = 2 × 4.75 PoVo = 19/2PoVo. Matches (b).
