Question

An unusual heat engine combines four different processes to acchieve a complete engine cycle shown below. there is a 1.60 moles of gas used in the engine, and the gas behaves like a monatomic ideal gas. Each engine cycle takes 0.020s to complete and involves to absorption of 4.73x10^4 J of heat to the outside enviroment.

temperature pressure volume

A 1800 K 6.0 x 10^5 Pa 0.0400 m^3

B 1800 K 2.9 x 10^5 Pa 0.0825 m^3

C 1175 K 1.0 x 10^5 Pa 0.157 m^3

D 300 K 1.0 x 10^5 Pa 0.0400 m^3

a)how much work is done by the gas as the gas expands at a constant temperature from A to B?

b) how much work is done by the gas as it expands adiabatically from B to C?

c)how much work is done as the gas is compressed from C to D?

d) what is the efficiency of this engine and how does this compare to the maximum theoretical efficiency of an engine operation between the maximum and minimum temperature of this system?

e)how much mechanical power does this engine generate assuming no energy is lost due to friction?

for some reason i cant upload the picture but i put in a table with the data,

Answer 1

a)

A to B = isothermal process

W = Pa*Va ln (Vb / Va)

= 6*10^5 *0.04 ln (0.0825 / 0.04)

= 17374.1 J

b)

B to C = adiabatic expanson

W = (Pb*Vb - Pc*Vc) / (n - 1).....................for monoatomic gas n = 1.67

= (2.9*10^5 *0.0825 - 1.0*10^5 *0.157) / (1.67 - 1)

= 12276.1 J

c)

C to D = isobaric compression

W = Pc*(Vd - Vc)

= 1.0*10^5 *(0.04 - 0.157)

= -11700 J

d)

Net work = 17374.1 + 12276.1 - 11700

= 17950.2 J

= 17.95 kJ

Heat rejection = 4.73*10^4 J = 47.3 kJ

Heat addition = W + Heat rejection

= 17.95 + 47.3

= 65.25 kJ

Efficiency = W / Heat addition

= 17.95 / 65.25

= 0.275

Carnot efficiency = 1 - T_low / T_high

= 1 - 300 / 1800

= 0.833

e)

Power = W / time

= 17.95 / 0.02

= 897.5 kW