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Process Calculations
Laws of Thermodynamics
GATE 2012
Hard

An insulated, evacuated container is connected to a supply line of an ideal gas at pressure Ps, temperature Ts and specific volume vs. The container is filled with the gas until the pressure in the container reaches Ps. There is no heat transfer between the supply line to the container, and kinetic and potential energies are negligible. If CP and CV are the heat capacities at constant pressure and constant volume, respectively (γ=CP/CV), then the final temperature of the gas in the container is

  • γTs
  • BTs
  • C(γ−1)Ts
  • D(γ−1)Ts/γ

Explanation

For adiabatic filling of an evacuated, insulated tank from a supply line, the energy balance reduces to hs=ufinal (the supply enthalpy equals the final internal energy in the tank). For an ideal gas, CpTs=CvTfinal ⟹ Tfinal=(Cp/Cv)Ts=γTs.

Source: GATE CH 2012 (2012)

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