Problem 4.079 SI A rigid tank whose volume is 3 m3, initially containing air at 1 bar, 295 K, is connected by a valve to a large vessel holding air at 6 bar, 295 K. The valve is opened only as long as required to fill the tank with air to a pressure of 6 bar and a temperature of 320 K. Assuming the ideal gas model for the air, determine the heat transfer between the tank contents and the surroundings, in kJ.

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cjmejiab cjmejiab · Answer 1 · 2019-11-11T06:05:20+01:00

Answer:

[tex]Q_{cv} = -1007.86kJ[/tex]

Explanation:

Our values are,

State 1

[tex]V=3m^3\\P_1=1bar\\T_1 = 295K[/tex]

We know moreover for the tables A-15 that

[tex]u_1 = 210.49kJ/kg\\h_i = 295.17kJkg[/tex]

State 2

[tex]P_2 =6bar\\T_2 = 296K\\T_f = 320K[/tex]

For tables we know at T=320K

[tex]u_2 = 228.42kJ/kg[/tex]

We need to use the ideal gas equation to estimate the mass, so

[tex]m_1 = \frac{p_1V}{RT_1}[/tex]

[tex]m_1 = \frac{1bar*100kPa/1bar(3m^3)}{0.287kJ/kg.K(295k)}[/tex]

[tex]m_1 = 3.54kg[/tex]

Using now for the final mass:

[tex]m_2 = \frac{p_2V}{RT_2}[/tex]

[tex]m_2 = \frac{1bar*100kPa/6bar(3m^3)}{0.287kJ/kg.K(320k)}[/tex]

[tex]m_2 = 19.59kg[/tex]

We only need to apply a energy balance equation:

[tex]Q_{cv}+m_ih_i = m_2u_2-m_1u_1[/tex]

[tex]Q_{cv}=m_2u_2-m1_u_1-(m_2-m_1)h_i[/tex]

[tex]Q_{cv} = (19.59)(228.42)-(3.54)(210.49)-(19.59-3.54)(295.17)[/tex]

[tex]Q_{cv} = -1007.86kJ[/tex]

The negative value indidicates heat ransfer from the system