Mumbai University > Mechanical Engineering > Sem 5 > IC Engines

Marks: 10M

Year: May 2016

A perfect gas at 1 bar and 290 K undergoes ideal diesel cycle. The maximum pressure of the cycle is 50 bar. The volume at the beginning of compression is 1m3 and after constant pressure heating is 0.1m3. Determine the temperature at all salient points of the cycle and also find out the efficiency of the cycle. Take γ = 1.4 for the gas.

${T_1} = 290K,{p_1} = 1bar{\text{ and }}{{\text{v}}_1} = 1{\text{ }}{{\text{m}}^3}$ $${T_2} = {T_1}{\left( {\frac{{{p_2}}}{{{p_1}}}} \right)^{\frac{{\gamma - 1}}{\gamma }}} = 290{\left( {\frac{{50}}{1}} \right)^{\frac{{0.4}}{{1.4}}}}$$

$$ = 290 \times {50^{0.286}}$$

$${T_2} = 887.77K$$

$$\frac{{{p_1}{v_1}}}{{{T_1}}} = \frac{{{p_2}{v_2}}}{{{T_2}}}$$

$${v_2} = \frac{{1 \times 887.77 \times 1}}{{50 \times 290}} = 0.06{m^3}$$

$$\frac{{{v_2}}}{{{T_2}}} = \frac{{{v_3}}}{{{T_3}}}$$

$${T_3} = 887.77 \times \frac{{0.1}}{{0.06}}$$

$${T_3} = 1480K$$

$${T_4} = {T_3}{\left( {\frac{{{v_3}}}{{{v_4}}}} \right)^{\gamma - 1}}$$

$${T_4} = 1480{\left( {\frac{{0.1}}{1}} \right)^{0.4}}$$

$${T_4} = 589.04K$$

$$\eta = 1 - \frac{{\left( {{T_4} - {T_1}} \right)}}{{\gamma \left( {{T_4} - {T_1}} \right)}} = 1 - \frac{{\left( {589.04 - 290} \right)}}{{1.4\left( {1480 - {{887.7}_1}} \right)}}$$

$$\eta = 0.6393 = 63.93\% $$