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Air in a rigid tank is at 100 kPa, 300 K with a volume of 0.75 m3. The tank is heated to 400 K, state 2. Now one side of the tank acts as a piston, letting the air expand slowly at constant temperature to state 3 with a volume of 1.5 m3. Find the pressure at states 2 and 3. Find the total work and total heat transfer.
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We are given following for Air:

T1 = 300 K

T3 = T2 = 400K

P1 = 100kPa

V1 = V2 = 0.75 m3

V3 =1.5m3

From ideal gas EOS we can calculate air mass:

P1.V = m.R.T1

From table, corresponding to Air:

We can find term for stage 2 pressure using ideal gas EOS:

P1.V = m.R.T1

P2.V = m.R.T2

\(\frac{P_1}{T_1}\,=\frac{P_2}{T_2}\)

P2 = \(\frac{P_1\,.\,T_2}{T_1}\) = \(\frac{100\,.\,400}{300}\)

P2 = 133.3kPa

We can find term for term for stage 3 pressure using ideal gas EOS for constant temperature Process:

P3.V3 = m.R.T

P2.V2 = m.R.T

P2.V2 = P3.V3 =

P3 = 66.7kPa

Work done in Process 1-2 is equal zero, because it is constant volume process:

W1-2 = 0

Work done in process 2-3 :

Total work done in Process is equal to :

W = W1-2 + W2-3 = 69.3kJ

W = 69.3kJ

Total heat transfer is given by :

Q = m(u3-u1) + W

Q = m.Cv.ΔT + W

From Properties of ideal gas table we can find heat capacity of air :

Cv = 0.717\(\frac{kJ}{kgK}\)

Q = m.Cv.(T3-T1) + W = 0.871.0717.(400-300) + 69.3 = 131.75kJ

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