An initially empty, rigid, insulated container is filled with air from a constan

Question

An initially empty, rigid, insulated container is filled with air from a constant pressure, Pl, and temperature, Tl, supply line. When filled, the air pressure in the vessel matches that in the line. The final temperature of the air in the vessel is given by which of the following equations?

An initially empty, rigid, insulated container is filled with air from a constant pressure, P1, and temperature, T1, supply line. When filled, the air pressure in the vessel matches that in the line. The final temperature of the air in the vessel is given by which of the following equations? a. T_f = cpT_I/cv b.T_f = T_I c. T_f = cvT_I/cp d. T_f = RT_I/cv

Explanation / Answer

Answer a.

Tf = cpT1/cv is the correct answer

Application of the conservation if mass will give delta m = mf - mi = mf

the first law thus reduces to delta m * hI = mf * uf , which when combined with conservation of mass becomes

hI = uf

Evaluating u and h with specific heat temperature products gives Tf = cpTi/cv

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