Extra Exam Equations

Extra Exam Equations

1. Frictionless piston-cyclinder

   • Total work transfer
     • SumW = w1-2 + w2-3 = P1 (v2 - v1)
       • v1 = RT1 / P1
   • Total heat transfer
     • Sum q = q1-2 + q2-3 = cv(T2 - T1) + P1 (v2 - v1) - cv (T2 - T3)
       • = cv (T3 - T1) + R (T2 - T1)
         • e.g. T3 = P3v3 / R

2. E.g. cooled at constant pressure until reaches volume. Gas then heated at constant vol until reaches pressure

   • Above: T1, P1 = P2, v2 = v3

3. Air velocity at outlet nozzle (adiabatic and frictionless)

   • Sum Q + Sum W = m-dot [(h2 - h1) + 0.5 (c^2 - c^2)] = m-dot [cp(T2 - T1) + 0.5 (c^2 - c^2)]
     • cp (T2 - T1) + 0.5(c^2 - c^2) = 0
       • c2 = square root of (c1^2 - scp (T2 - T1))

4. COP of a system

   • COPsys = Qin (fridge effect) / Qin (engine

5. Mass of air: PV = mRT1

   • m2 (final mass) - m1 (initial mass worked out)

6. Polytropic index if end state changes

   • P2/ P1 = (v1 / v2)^n = (T2 / T1)^(n/n-1)
     • (n/n-1) x ln (T2 / T1) = ln (P2 / P1)

7. Mass of sealed air in constant-volume gas thermometer

   • P1V1 / T1 = P2V2 / T2
     • mass = P1V1 / RT1

8. Height of water column equiv to pressure rises through pump

   • (P2 - P1) = pgh

9. Change in internal energy

   • = m . cv . (T2 - T1)

10. Change in enthalpy

    • = m . cp . (T2 - T1)

11. Flow rate of water when temp changes to T2

    • Power input (Win) x efficiency = m-dot x specific heat x (T2 - T1)

12. atm = Phg x g x mmHg

13. Heat energy transfer polytropic open system

    • q1-2 = (h2 - h1) + w1-2 = cp (T2 - T1) + w1-2

14. Find T2 when given pressure, T1 and velocities

    • m-dor (h2 - h1) + m-dot (v2^2 / 2 - v1^2 / 2) = 0
      • cp(T2 - T1) + (v2^2 / 2 - v1^2 / 2) = 0
    • Inlet and outlet area
      • v-dot = v x m-dot
        • A1 = v-dot / v1