Question

Two kilograms of air within a piston–cylinder assembly executes a Carnot power cycle with maximum and minimum temperatures of 800 K and 295 K, respectively. The heat transfer to the air during the isothermal expansion is 60 kJ. At the end of the isothermal expansion the volume is 0.4 m3. Assume the ideal gas model for the air. Determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kJ.

Answer 1

thermal efficiency, η= 0.63125

volume at the beginning of the isothermal expansion, V1 = 0.34011 m3

work during the adiabatic expansion, in kJ = 766.59 KJ

Step-by-step explanation:

To determine the thermal efficiency

The thermal efficiency of a heat engine gives an estimation of the amount of heat energy converted to work in the engine.

Thermal efficiency is given by: η= 1- (Tc/Th)

where, Tc= ambient temperature or the minimum temperature

Th= maximum temperature

from the given data:

minimum temperature = 295 K

maximum temperature = 800 K

η= 1- (295/800)

η= 0.63125

To determine the volume at the beginning of the isothermal expansion, in m3

We know, ΔU = Q − W.

where, ΔU is the change in internal energy of the system.

Q= mRT In (V2/V1)

Where, V1 = volume at the beginning of the isothermal expansion

V2 = = volume at the end of the isothermal expansion

Therefore, V1 = V2 / (Q/mRT)

V1= 0.4/ ((60000/ (2 x 287 x 800))

V1 = 0.34011 m3

where, isothermal expansion given is 60 kJ

isothermal expansion the volume given is 0.4 m3

To determine the work during the adiabatic expansion, in kJ.

Work during the adiabatic process is given by

W = − ΔU

where, ΔU is the change in internal energy of the system

W at the first and second process = - 2 x 759 ( 295 - 800)

= 766590J = 766.59 KJ