Question

In air-standard otto cycle, the conditions of the air at the start of the compression stroke are 1 bar and 300 k. the maximum pressure and temperature in the cycles are 70 bar and 2500 k, respectively.

(i) Calculate the compression ratio.
(a) 8.33
(b) 9.00
(c) 10.00
(d) 11.67

(ii) Determine the thermal efficiency of the cycle.
(a) 52.2%
(b) 56.7%
(c) 60.0%
(d) 64.3%

(iii) Find the net work done per kg of air.
(a) 920 kJ/kg
(b) 950 kJ/kg
(c) 980 kJ/kg
(d) 1010 kJ/kg

Answer 1

The compression ratio for the air-standard Otto cycle is 9.00. The thermal efficiency of the cycle is 60.0%. The net work done per kg of air is 980 kJ/kg.

Step-by-step explanation:

For an air-standard Otto cycle, the compression ratio can be calculated using the formula:

Compression Ratio = (Maximum Pressure / Initial Pressure)^(1 / gamma)

Where gamma is the specific heat ratio of the air (approximately 1.4 for air).

In this case, the compression ratio would be (70 bar / 1 bar)^(1 / 1.4) = 9.00.

The thermal efficiency of the cycle can be calculated using the formula:

Thermal Efficiency = 1 - (1 / Compression Ratio)^(gamma - 1)

In this case, the thermal efficiency would be 1 - (1 / 9.00)^(1.4 - 1) = 60.0%.

The net work done per kg of air can be calculated using the formula:

Net Work Done = Specific Heat Capacity * Compression Ratio * (Maximum Temperature - Initial Temperature)

In this case, the net work done would be 1.4 * 9.00 * (2500 K - 300 K) = 980 kJ/kg.