Question

2 moles of compressed air (diatomic gas) in a cylinder under the initial condition T1=573K p1=500kPa.

Found v1=0.019m^3 but can not remember then how to find V2. I think that it has something to do with T1=T2 condition then P2 can be found.... but stuck on how to proceed so with FULL written explanations with working would be much appreciated!

All question info on practice exam below - note ISOTHERMAL EXPANSION. for part ii which after an explanation first.

Two moles of compressed air (diatomic gas) are in a cylinder under the initial condition: T1= 573 K and p1 = 500 kPa. (i) Find the initial volume of the air V1. [1 mark] The compressed air expands isothermally to state 2: p2 = 200 kPa. (ii) Find V2 . [1 mark] (iii) Determine ΔEint, Q received by the system and W, the work done by the system in this isothermal process. [3 marks] (iv) If the air expands isobarically to the same V2 as in (ii) above from the initial state 1, will the system receive more heat than it did in the previous isothermal process? Explain your meaning. [2 marks] (v) Show those two processes (isothermal and isobaric) on a p − V diagram. [1 mark] Additional Information: The average total translation kinetic energy of a molecule of a gas is 1/2 mv^2 = 3/2 kBT , where kB is Boltzman’s constant, v is the root-mean-square speed. CV = f/2 R, f : number of degrees of freedom. Equation of state of ideal gas pV = nRT where R = 8.314 J K–1 mol–1 . Work done by gas W = pdV = nRT ln Vf Vi ⎛ ⎝ ⎜ ⎞ ⎠ ∫ ⎟ , (in an isothermal process). Internal energy of an ideal gas Eint = nCVT.

Answer 1