Question

The compression ratio is 10 in the air standard Otto cycle. Pressure at the beginning of the compression stroke is 1XY kPa and the temperature is 15 ºC. The heat transfer to the air for each cycle is 18XY kJ / kg air. Draw the T-s and P-v diagrams. (x=9 y=8).

Note: Accept that specific temperatures do not change with temperature. Take k = 1.4 and Cp = 1.0031 kJ / kg-K.

a)

For question 1, we draw the temperature and pressure values ​​at the end of each condition in the cycle by drawing a table.

b)

Write the thermal efficiency for Question 1.

c)

For Question 1, write down the mean effective pressure. (Unit kPa)

d)

Calculate the efficiency of the Carnot machine operating between the maximum and minimum temperatures in Question 1.

Answer 1

Pressure = 198 kPa

Heat transferred to Air = 1898 kJ/ kg air

T₁ = 288 K

P-V Diagram

T-S diagram

P₂ = 198 kPa x (10)^1.4

P₂ = 4973.535 kPa

Performing an energy balance for the constant volume heat addition process (2--> 3), Eq3 is obtained.

Qin = u3 - u2 = Cv (T₃ -T₂)

Qin = 1898 = 0.718 ( T₃ - 723.4 )

T₃ = 3366.85 K

P₃ = P₂ (T₃ /T₂)

P₃ = 4973.535 kPa x ( 3366.85/ 723.4 )

P₃ = 23147.84 kPa

Since the process from 3 to 4 is isentropic, the temperature at state 4 can be determined using the ideal gas relation relating the temperature and specific volume ratios through k as shown in Eq

T₄ = T₃ x (V3/ V4)^k-1

T₄ = 3366.85 x (1/10)^1.4-1

T₄ = 1340.7 K

The pressure can be determined from the isentropic relation for an ideal gas, which relates the pressure and the specific volume ratios through k as shown in Eq

P₄ = P₃ x ( V3/ V4)^k

P₄ = 23147.84 kPa x (1/10 )^1.4

P₄= 921.53 kPa

  Qout = Cv ( T₄ - T₁ )

= 0.718 ( 1340.7 - 288 )

= 755.84 kJ/kg

Wnet = Qin - Qout

= 1898 - 755.84

= 1142.16 kJ/kg

(b) Thermal efficiency =( Wnet/Qin ) x100

= (1142.16/1898) x100

Thermal efficiency = 60.18 %

(c) The mean effective pressure (MEP) can be determined using Eq

MEP = Wnet/(V1-V2)

V1= RT1 /P1

V1 = (0.287 x 288 )/ 198

V1 = 0.4174 m³/kg

V2=V1/10 compression ratio 10

V2 = 0.04174

MEP = 1142.16 /(0.4174-0.04174)

MEP = 3040 kPa

(d) Efficiency of carnot machine

Efficiency = 1 - T₁/T₃

= 1- 288/3366.85

= 0.9145

Efficiency of carnot machine = 91.45 %