SSC JE Mechanical Engineering 2018 Set 1 Paper

Question : 146 of 200

Marks: +1, -0

A gas is compressed frictionless from an initial state of y m

^{3}

and 1 MPa to a final state of 0.2 m

^{3}

and 1 MPa. There is a transfer of 40 kJ of heat from the gas and a drop of 20kJ in internal energy.
What is the initial state volume of the gas?

Solution:

Given:

P_1 = P_2 = 1 \Mpa

v_1 = ym^3 , v_2 = 0.2,

dQ = -40 K = 40×10^3

dv = -20 K = 20×10^3

Workdone at constt pressure W = P.dv

= 1×10^6 (y – 0.2)

From relation -
dQ = dv + dw
⇒

-40 = -20 + 1×10^6 (y -0.2)

⇒

-20 ×10^3 = 1×10^6 (y -0.2)

⇒

y = 0.2 +20/1000 = 0.22

⇒

y = 0.22 m^3

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