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ENGR5003 / Week 2
ENGR217 2025 Q2Past paperOld spec ENGR2172:130 marks36 min

ENGR217 Summer 2025 Q2[VALID] official answers

A 12 litre cryogenic tank initially contains air at 1 bar at a temperature of 293 K. The tank is then charged by a high pressure gas main at a temperature of 300 K to a final pressure of 250 bar. You may assume that the air is an ideal gas and the tank is rigid. You may also assume that Rg=0.287 kJ/kg/KR_g = 0.287\ \mathrm{kJ/kg/K} and γ=1.4\gamma = 1.4.

Formulas you may need
  • Ideal gas: pV=mRgTpV = mR_gT (on the formula sheet)
  • cv=Rgγ−1c_v = \dfrac{R_g}{\gamma-1}, cp=γRgγ−1c_p = \dfrac{\gamma R_g}{\gamma-1}, dU=mcv dTdU = mc_v\,dT, dH=mcp dTdH = mc_p\,dT (u=cvTu = c_vT, h=cpTh = c_pT) (on the formula sheet)
  • Unsteady flow: dU=(h+C22+gZ)indmin−(h+C22+gZ)outdmout+dQ−dWdU = \left(h + \tfrac{C^2}{2} + gZ\right)_{in} dm_{in} - \left(h + \tfrac{C^2}{2} + gZ\right)_{out} dm_{out} + dQ - dW (on the formula sheet)
  • SFEE: Q˙−W˙=m˙[(h+C22+gZ)out−(h+C22+gZ)in]\dot Q - \dot W = \dot m\left[\left(h + \tfrac{C^2}{2} + gZ\right)_{out} - \left(h + \tfrac{C^2}{2} + gZ\right)_{in}\right] (on the formula sheet)
  • Isochoric process: dW=0dW = 0, dQ=dU=mcv dTdQ = dU = mc_v\,dT (on the formula sheet)
  • Entropy change: Δs=cvln⁡T2T1+Rgln⁡v2v1\Delta s = c_v\ln\dfrac{T_2}{T_1} + R_g\ln\dfrac{v_2}{v_1} (on the formula sheet)
  • Reversible heat transfer dQ=T dSdQ = T\,dS (given in the question)
  • Rigid tank charged from a main: m2u2−m1u1=hin(m2−m1)m_2u_2 - m_1u_1 = h_{in}(m_2 - m_1) (learn this derivation)
  1. (a)
    Determine the initial and final mass of gas in the tank as well as the final temperature, assuming an adiabatic charging process. You should treat this as an unsteady flow problem
    [8]
  2. (b)
    The tank is allowed to cool back to 293 K. Determine the heat rejected and the pressure change of the process. Given that no work is done during the cooling process, determine the entropy change, given that ΔQ=mcp dT=T dS\Delta Q = m c_p\, dT = T\, dS.
    [8]
  3. (c)
    The tank is then discharged through a valve. We can neglect the flow velocity of the gas in the tank, but after the valve, the gas flow velocity is 150 m/s. Determine the specific enthalpy of the gas leaving the tank and the temperature change. You may assume there is no heat exchange or work done during the discharging process
    [8]
  4. (d)
    From the calculations in part (c), discuss whether it is reasonable or not to consider the kinetic energy term and justify your answer. What is the maximum flow velocity that can be achieved
    [6]