THERMODYNAMIC

Question

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.

Answer 1

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:

W_1-2 = 0

Work done in process 2-3 :

Total work done in Process is equal to :

W = W_1-2 + W_2-3 = 69.3kJ

W = 69.3kJ

Total heat transfer is given by :

Q = m(u₃-u₁) + W

Q = m.C_v.ΔT + W

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

C_v = 0.717\(\frac{kJ}{kgK}\)

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