GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 39 of 65

Marks: +1, -0

An engine working on air standard Otto cycle is supplied with air at

0.1 {MPa}

and

35^{∘} {C}

. The compression ratio is

8 .

The heat supplied is

500 {kJ} {/} {kg}

. Property data for air:

c_{ρ}=1.005 {kJ}{/} {kgK}, c_{v} 0.718 {kJ} {/} {kgK}, R=0.287 {kJ} {/} {kgK} .

The maximum temperature (in

{K}

) of the cycle is (correct to one decimal place).

Solution:

P_{1}=0.1 {MPa}_{f} T_{1}=35^{∘} {C}=308 {K}

\;{V_{1}}/{V_{2}}=n=8

Q_{s}=500 {k}j {/} {kg}

c_{p}=1.005 {kJ} {/} {kgK}

c_{v}=0.718 {kJ} {/}{kgK}

R=0.287 {kJ} {/} {kgK}

y=\;{c_{p}}/{c_{v}}=1.399=1.40

T_{3}=T_{nox}=?

For process

1-2

\;{T_{2}}/{T_{1}}=(\;{V_{1}}/{V_{2}})^{γ-1}=8^{0.4}

T_{2}=707.6 {K}

For process

2 → 3

Q_{s}=C_{V}(T_{3}-T_{2})=500 {kJ} {/}{kg}

0.718(T_{3}-707.6)=500

T_{3}=1403.97 {K}

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