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PY 2: GATE ME 2020 Official Paper: Shift 2

Option 1 : -26.3

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__Concept:__

The change in entropy of gas at given pressure is,

\({s_2} - {s_1} = {C_p}\ln \left( {\frac{{{T_2}}}{{{T_1}}}} \right) - R\ln \left( {\frac{{{P_2}}}{{{P_1}}}} \right)\)

Where, s_{2} - s_{1} = change in entropy, C_{p} = specific heat at constant pressure, R = gas constant

T = temperature, P = pressure

__Calculation:__

m = 1 kg, P_{1} = 1 bar, P_{2} = 3 bar, T_{1} = 27°C = 27 + 273 = 300 K, T_{2} = 127°C = 127 + 273 = 400 K

γ = 1.4, R = 287 J/kg.K

\({C_p} = \frac{{\gamma R}}{{\gamma - 1}} = \frac{{1.4\; \times \;287}}{{1.4\; - \;1}} = 1005\;J/kg.K\)

\(\therefore {s_2} - {s_1} = 1005 \times \ln \left( {\frac{{400}}{{300}}} \right) - 287 \times \ln \left( {\frac{3}{1}} \right)\)

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