SSC JE Mechanical Engineering 11 Oct 2020 Shift 1 Papers

Question : 163 of 200

Marks: +1, -0

Air is compressed entropically in a single stage single acting compressor from an initial condition of 1 bar and 30°C to 5 bar. If γ = 1.4 and R = 287 J/kg.K for air, work of compression for unit mass rate of air is (Use (5)

^0.286

= 1.584)

198.3 kW
17.769 kW
177.69 kW
205.8 kW

Validate

Solution:

P_1 = 1

bar,

P_2 = 5

bar, R = 287 J/kgK = 0.287 kJ/kgK, γ = 1.4, m = 1 kg/s,

T_1 = 30 + 273 = 303

K and

(0.5)^{0.286} = 1.584

Subsituting all the values in above Win equation

{W}_{\text "in "}=({\γ}/{\γ-1}) {mRT}_{1}[({{P}_{2}}/{{P}_{1}})^{{\γ-1}/{\γ}}-1]

{W}_{\text "in "}=({1.4}/{1.4-1}) \×1 \×0.287 \×303

\×[({5}/{1})^{{1.4-1}/{14}}-1]

{W}_{\text "in "}=(3.5) \×1 \×0.287 \×303

\×[(5)^{0.286}-1]

{W}_{\text "in "}=(3.5) \ × 1 \×0.287 \

×303 \×[0.584]

{W}_{\text "in "}=177.74 {kW} \≈177.69 {kW} .

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