To determine Prove the equation c p , g − c p , f = T ( ∂ ( h f g / T ) ∂ T ) P + v f g ( ∂ P ∂ T ) sat . Explanation Write the given equation. c p , g − c p , f = T ( ∂ ( h f g / T ) ∂ T ) P + v f g ( ∂ P ∂ T ) sat (I) Here, temperature is T , pressure is P , specific volume is v , specific heat at constant pressure is c P , vaporization enthalpy is h f g , vaporization specific volume is v f g , subscripts g , f indicates the gaseous and fluid states and symbol ∂ indicates the partial derivative of variables. Write the formula for specific heat at constant pressure ( c P ) . c p = ( ∂ h ∂ T ) P (II) Write the relation of Clapeyron equation. ( d P d T ) sat = h f g T v f g (III) The vaporization enthalpy ( h f g ) is expressed as follows. h f g = h g − h f (IV) Conclusion: Divide Equation (IV) by T on both sides. h f g T = h g − h f T = h g T − h f T (V) Partially differentiate Equation (V) with respect to temperature ( T ) at constant pressure. ∂ ∂ T ( h f g T ) P = ∂ ∂ T ( h g T − h f T ) P ( ∂ ( h f g / T ) ∂ T ) P = [ ∂ ∂ T ( h g T ) ] P − [ ∂ ∂ T ( h f T ) ] P = 1 T ( ∂ h g ∂ T ) P − h g ( 1 T 2 ) − [ 1 T ( ∂ h f ∂ T ) P − h f ( 1 T 2 ) ] = 1 T ( ∂ h g ∂ T ) P − h g T 2 − 1 T ( ∂ h f ∂ T ) P + h f T 2 = 1 T ( ∂ h g ∂ T ) P − 1 T ( ∂ h f ∂ T ) P − h g T 2 + h f T 2 = 1 T ( ∂ h g ∂ T ) P − 1 T ( ∂ h f ∂ T ) P − h g − h f T 2 (VI) Refer Equation (II) and (IV). Substitute c p , g for ( ∂ h g ∂ T ) P , c p , f for ( ∂ h f ∂ T ) P , and h f g for h g − h f in Equation (VI)

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Chapter 12.6, Problem 30P

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Prove the equation cp,g−cp,f=T(∂(hfg/T)∂T)P+vfg(∂P∂T)sat.

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Chapter 12.6, Problem 29P

Chapter 12.6, Problem 31P

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As shown in the figure below, a ring is used to suspend a load and is supported by Cable OA and Spring OB. Given that the tension in Cable OA is 400 N, what is the weight of the load being supported? Assume the system is in static equilibrium.

4. (a) State the conditions that must be met to ensure dynamic balance is achieved for long rotors. (b) A rotor carries three out-of-balance discs in planes A, B and C as shown in Figure 4. The out-of- balance mass x radius products of the rotor discs are tabulated in Table 4. The shaft is to be dynamically balanced by adding balancing masses in planes P and Q, spaced along the shaft at a distance da = 800 mm. Determine the magnitude mara and angular position of the balancing mass x radius product that must be added to plane Q. MBB Ов θε mdc Мага End View on Plane P P MBB MATA dA dB dc do Figure 4 moc Table 4 MATA = 0.6 kg mm 6A = 0° d₁ = 200 mm mers = 0.2 kg mm 6g = 45° dB = 400 mm mcrc = 0.4 kg mm Bc=240° dc = 600 mm Ans. (b) = 110.5°, moro = 0.2 kg mm

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