Question

A sample consisting of 65.0 g of xenon is confined in a container at 2.00 atm and 298 K and then allowed to expand adiabatically (a) reversibly to 1.00 atm, (b) against a constant pressure of 1.00 atm. Calculate the final temperature and the expansion work at each case. Use the fact that xenon is a monoatomic gas.

Answer 1

[a]. - 445.45J,

[b]. - 367.92 J

Step-by-step explanation:

The following parameters are given in the question above. These information are used in solving this problem.

The mass of Xenon = 65.0 g of xenon, pressure = 2.00 atm, temperature = 298 K.

The number of moles of xenon = mass/ molar mass = 65g/ 131.293= 0.495.

The cp= 3/2 R, cp =3/2R + R = 5/2 R.

j = cp/cv = 3/2.

[a]. The final temperature,T2 = (2)^-2/3 × (298)^5/3 = T2^5/3.

Final temperature,T2 = 225.84K.

Expansion work = nCv [ T₂ - T₁] = 0.495 × 3/2 × 8.314 × [ 225.84 - 298] = - 445.45J.

(b). The final temperature can be Determine as;

3/2( T2 - 298k) = - 1 (T2 /1 - 298/2).

3/2(T2 - 298) = - T2 + 149K.

3T2 - 894 = - 2T2 +298K.

T2 = 238.4 K.

Workdone= nCv (T2 - T1) = 0.495 × 3/2 × 8.314 (238.4 - 298) = - 367.92 J.