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ENGR5003 / Week 1
Week 1 Q3Exercise sheetCurrent spec2:212 min

ENGR5003 Week 1 workshop sheet Q3

For the following diagram of a Rankine cycle (Figure Q3), estimate the thermal efficiency, given that ΔQ=m∫T ds\Delta Q = m\int T\,ds.

Remember that ηth=WnetQin=1−QoutQin\eta_{th} = \dfrac{W_{net}}{Q_{in}} = 1 - \dfrac{Q_{out}}{Q_{in}}. Also for the isobaric heat addition process (2→32 \to 3), assume that the function is: T={107.5 s+6.25,s≤2.5275,2.5<s≤6.0T = \begin{cases} 107.5\,s + 6.25, & s \le 2.5 \\ 275, & 2.5 < s \le 6.0 \end{cases} and for the isobaric heat rejection (4→14 \to 1), T=30T = 30, s=[0.5,6.25]s = [0.5, 6.25]. Here temperatures are in Celsius.

Figure Q3: Rankine cycle on a T-s diagram for water (50 bar boiler, 0.06 bar condenser), states 1-4 marked.
Figure Q3: Rankine cycle on a T-s diagram for water (50 bar boiler, 0.06 bar condenser), states 1-4 marked.
Formulas you may need
  • Heat from a reversible path: q=∫T dsq = \int T\,ds with TT in kelvin (given in the question)
  • Thermal efficiency: ηth=WnetQin=1−QoutQin\eta_{th} = \dfrac{W_{net}}{Q_{in}} = 1 - \dfrac{Q_{out}}{Q_{in}} (on the formula sheet)