Question

One mole of air undergoes a Carnot cycle. The hotreservoir is at 800oC and the cold reservoir is at 25oC. The pressure ranges between 0.2bar and 60 bar. Determine the net work produced and the efficiency of the cycle.

Answer 1

The net work produced = -36737.52 J

The efficiency of the cycle = 72.2%

Step-by-step explanation:

Given that :

The temperature of the hot reservoir
`(T__H})` = 800 °C = (800+273)K

The temperature of the cold reservoir
`(T__C})` = 25 °C (25+273)K

Pressure
`(P__A})` = 0.2 bar

Pressure
`(P_B})` = 60 bar

Rate constant (R) = 8.314

Determination of the efficiency of the cycle (η) is given by the formula:

(η) =
`1-(T__C)/(T__H)`

= 1 -
`((800+273)K)/((25+273)K)`

= 0.722

= 72.2 %

∴ The efficiency of the cycle = 72.2 %

However, the heat given along the initial hot isothermal path
`(Q__H})` is equal to the work done which is given by the equation;

`Q__H}=nRT__H}In(V_b)/(V_a)`

`Q__H}=nRT__H}In(P_a)/(P_b)`

substituting our data from the given parameters above; we have:

`= 1 * 8.314 * (800+273) *In ((0.2)/(60) )`

= -50882.99 J

To determine the net work produced; we have:

`W_(net)` = η
`Q__H`

= 0.722 × (-50882.99 J)

= -36737.52 J

∴ The net work produced = -36737.52 J