Question

Consider a 35-L evacuated rigid bottle that is surrounded by the atmosphere at 100 kPa and 22 ℃. A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle during this filling process. -pinterest\.\*

Answer 1

Answer:

3.5 KJ

Explanation:

Energy balance equation is given as;

E_in - E_out = ΔE_system

Thus;

Q_in = (m_2•u_2) - (m_i•h_i)

Now, m_i = m_2

Tbus;

Q_in = (m_2•u_2) - (m_2•h_i)

Q_in = m_2(u_2 - h_i)

Now mass of the air in the bottle is given as;

m_2 = (P_2•V)/(R•T2)

From table A-1 attached, R = 0.287 KJ/Kg.k

We are given;

P_2 = 100 kPa

V = 35 L = 0.035 m³

T2 = 22°C = 22 + 273 K = 295 K

Thus;

m_2 = (100 × 0.035)/(0.287 × 295)

m_2 = 0.04134 kg

Now, from table A-17 attached, at Temperature of 295 K, we have;

Internal energy; u2 = 210.49 KJ/Kg

Enthalpy; h_i = 295.17 KJ/Kg

From earlier, we saw that;

Q_in = m_2(u_2 - h_i)

Thus;

Q_in = 0.04134(210.49 - 295.17)

Q_in = -3.5 KJ

Thus, Q_out = 3.5 KJ

So, the net heat transfer = 3.5 KJ