Question

Please help me with this Thermal problem. Thanks

Problem 1. Consider a well-insulated tank with constant volume, V. The tank is initially at vacuum ("State 1", mi-0). Surrounding the tank is an ideal gas, with constant cv and k and gas constant R. The pressure Pin and temperature Tin of the ideal gas surrounding the tank are constant. A very tiny hole is punched into the tank and air fills the tank with a time-dependent mass flow rate, mi(), until the pressure inside the tank equals that in the surrounding environment (P2-Pin). (la) Solve for the final temperature of the tank, T2, and (1b) the final mass of air inside the tank, m2, as a function of known variables (V, cv, k, R, Pin and/or Tin). The solution has been started for you here: Mass Balance) (dm)-Σ¡nmin-Lut mout ll Assume: l inlet, no outlets ㈜cv_rhin f Simplified mass balance (Energy Balance) -WmnAssume: No work; No heat transfer (note: inp2, you cannot assume this) CV dcynhn Plug in the simplified mass balance equation. (a )cv = hin ㈜cv "Integrate from State l to State 2 Notehn is constant, since ideal gas with T. AU-hmdm ll Keep going, recall U-um; h-u + pv; pv-RT, how Δυ relates to ΔΤ when cv is constant, etc. Problem 2. Consider a perfectly thermally conducting tank with constant volume, V. The tank is initially at vacuum ("State 1", m0). Surrounding the tank is an ideal gas, with constant cv and k and gas constant R. The pressure Pin and temperature Tin of the ideal gas surrounding the tank are constant. A very tiny hole is punched into the tank and air fills the tank with a time-dependent mass flow rate, m(t), until the pressure inside the tank equals that in the surrounding environment (P2. The temperature inside the tank is always equal to the surrounding environment (T1T2-Tin). (2a) Solve for the heat transfer, Q, as a function of known variable ( cv, k, R, Pim and/or Tn. (2b) Is heat transferred into or out of the tank, in order to maintain constant temperature?

Answer 1