GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 63 of 65

Marks: +1, -0

An air standard Otto cycle has thermal efficiency of

0.5

and the mean effective pressure of the cycle is

1000 {kPa}

. For air, assume specific heat ratio

γ=1.4

and specific gas constant

R=0.287

kJ/kg.K, If the pressure and temperature at the beginning of the compression stroke are 100

{kPa}

and

300 {K}

, respectively, then the specific net work output of the cycle is _________ kJ/kg(round off to two decimal places).

Solution:

Given data

P_{1}=100 {kPa}, {T}_{1}=300 {K}

, mep

=1000 {kPa}, γ=1.4

, efficiency

(η)=0.5, {R}=0.287 {kJ} {/} {kg}- {K}

Using

P_{1} V_{1}=R T_{1}

{V}_{1}=\;{0.287 × 300}/{100}=0.861 {m}^{3} {/} {kg}

Efficiency

(η)=1-\;{1}/{(r)^{r-1}}

where,

r

is the compression ratio

=V_{1} {/} V_{2}

1-\;{1}/{(r)^{γ-1}}=0.5

1-\;{1}/{(r)^{1.4-1}}=0.5

Or,

{r}=5.657

{V}_{1} {/} {V}_{2}=5.657

⇒ V_{2}=0.1522 {m}^{3} {/} {kg}

Swept volume

= {V}_{1}- {V}_{2}=0.861-0.1522=0.7088 {m}^{3} {/} {kg}

Went

=

Swept volume

× {mep}=0.7088 × 1000=708.8 {kJ} \/ {kg}

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