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ENGR5003 / Week 2
Week 2 Q3Exercise sheetCurrent spec2:215 min

ENGR5003 Week 2 workshop sheet Q3

Consider a rigid vessel of 0.15 m30.15\ \mathrm{m^3} with an initial pressure of 0.6 bar at 320 K. High pressure air at 271 K is charged into the vessel until the pressure is 25 bar. Assume γ=1.4\gamma = 1.4 and that the charging process is adiabatic.

Formulas you may need
  • Unsteady flow energy equation: Q−W=(m2u2−m1u1)−∑min(h+c22+gz)in+∑mout(h+c22+gz)outQ - W = (m_2u_2 - m_1u_1) - \sum m_{in}\left(h + \tfrac{c^2}{2} + gz\right)_{in} + \sum m_{out}\left(h + \tfrac{c^2}{2} + gz\right)_{out} (on the formula sheet)
  • Ideal gas: u=cvTu = c_vT, h=cpTh = c_pT, γ=cp/cv\gamma = c_p/c_v, pV=mRgTpV = mR_gT (on the formula sheet)
  • cv=Rgγ−1c_v = \dfrac{R_g}{\gamma - 1} (on the formula sheet)
  • Isochoric closed system: Q=ΔU=mcvΔTQ = \Delta U = mc_v\Delta T (on the formula sheet)
  1. (a)
    Determine the final temperature of the system.
  2. (b)
    What mass of gas was added?
  3. (c)
    The gas in the vessel is allowed to cool down to 320 K again. How much heat is rejected during this cooling process? You may assume Rg=0.287 kJ/kg/KR_g = 0.287\ \mathrm{kJ/kg/K}