Question

A piston contains 600 moles of an ideal monatomic gas that initally has a pressure of 2.35 x 10 Pa and a volume of 1.8 m5. The piston is connected to a hot and cold reservoir and the gas goes through the following quasi-static cycle accepting energy from the hot reservoir and exhausting energy into the cold reservoir 1. The pressure of the gas is increased to 5.35 x 105 Pa while maintaining a constant volume. 2. The volume of the gas is increased to 8.8 m3 while maintaining a constant pressure. 3. The pressure of the gas is decreased to 2.35 x 105 Pa while maintaining a constant volume 4. The volume of the gas is decreased to 1.8 m3 while maintaining a constant pressure. It may help you to recall that Cv 12.47 J/K/mole and Cp 20.79 J/K/mole for a monatomic ideal gas, and that the Avagadros number (6.022 x 1023) times the number of moles of the gas - number of gas molecules is equal to

Answer 1

The quasi-static cycle described features two steps that transfer heat into the gas (1 & 2) and two steps out of the gas

(3 & 4).

1. The pressure of the gas is increased to 5.35 x 10⁵ Pa while maintaining a constant volume.

2. The volume of the gas is increased to 8.8 m³ while maintaining a constant pressure.
3. The pressure of the gas is decreased to 2.35x10⁵ Pa while maintaining a constant volume.
4. The volume of the as is decreased to 1.8 m³ while maintaining a constant pressure.

Point 1: P_min & V_min = 84.791K

Point 2: P_max & V_min = 193.036K

Point 3: P_max & V_max = 943.73K

Point 4: P_min & V_max = 414.536K

These are vital when discovering Qs since ∆T is required and to make the later equations simpler to pursue with as meager arithmetic errors avoided.

1) $\small Q_{in}$ to in steps 1 and 2 =

1.017 x 10 Qh nCAT(ptl, 2) nCpAT(pt2,3)

2)  
out
in steps 3 and 4 =
Qe=nC,AT(pt3,4)nCpAT(pt4, 1)

3)  To find Work done by gas:

  

Wy=AP x AV = 2.1 x 10J

4)  From the calculated Q_h and Q_c above, find efficiency:  

8.072x 100 =1- = 1- 1.017 x 107 = 0.206 Qh