Question

The minimum pressure and temperature of in an otto cycle are 100 kpa and 27°c. The amount of heat added to the cycle is 1500 kj/kg. Determine pressures and temperatures at all points of the air standard cycle. Also calculate the specific work and the thermal efficiency of the cycle for a compression ratio of 8:1.

Answer 1

Answer:

yes the right answer is 1500 kg

Answer 2

Given:-

$\text{Pressure}, P_{a}=100kPa\\\text{Temperature},T_{a}=27^{0}C=300K\\\text{Heat addition},Q_{a}=1500kJ/kg\\\text{specific heat ratio},\gamma=1.4$

$\text{compression ratio,}r=8$

To Find:-

pressure & temperature at all points and specific work and efficiency

Explanation:-

Consider abcd an otto cycle.

$\text{For adiabatic process a-b}:-\\\\\frac{T_{b}}{T_{a}}=r^{\gamma-1}\\\\\Rightarrow\frac{T_{b}}{300}=8^{1.4-1}\Rightarrow T_{b}=689.219K$

$Now,\\\\\frac{P_{b}}{P_{a}}=r^{\gamma}\\\\\Rightarrow\frac{P_{b}}{100}=8^{1.4}\Rightarrow P_{b}=1837.917kPa$

For constant volume process b-c:-

$\text{Heat addition at constant volume,} Q_{a}=C_{v}\times(T_{c}-T_{b})\\\\\Rightarrow1500=0.718\times(T_{c}-689.219)\RightarrowT_{c}=2778.355K\\\\Now,\\\\\frac{P_{b}}{T_{b}}=\frac{P_{c}}{T_{c}}\\\\\frac{1837.917}{689.219}=\frac{P_{c}}{2778.355}\Rightarrow P_{c}=7408.945kPa$