Question

A sample consisting of 2.5 moles of ideal gas (C_p,m =20.8 J/K) is initially at 3.25 atm and 300 K. It undergoes reversible adiabatic expansion until its pressure reaches 2.5 atm. Calculate the final volume, the final temperature, and the work done.

Answer 1

A sample consisting of 2.5 moles of ideal gas (C_p,m =20.8 J/K) is initially at 3.25 atm and 300 K. It undergoes reversible adiabatic expansion until its pressure reaches 2.5 atm. Calculate the final volume, the final temperature, and the work done

P1 = 3.25 atm P2 = 2.5 atm

T1 = 300 K

n = 2.5

Using Initial conditions and the formula PV = nRT, lets calculate V1

V1 = nRT/P

   = 2.5 moles * (0.0821 L-atm/mole*Kelvin) * 500

   3.25 atm

V1 = 31.6 L

--------------------------------------------------------------------

P1 = 3.25 atm P2 = 2.5 atm

V1 = 31.6 L V2 = ?

P1V1 = P2 V2

V2 = P1V1

P2

= 3.25 * 31.6

2.5

V2 = 41.1 L

------------------------------------------------------------

P2 = 2.5 atm V2 = 41.1 L T2 = ?

PV = nRT

PV = T

nR

2.5 atm * (41.1 L)

2.5 moles * (0.0821 L-atm/mole*K)

= 500.6 K

T2 = 501 Klevin