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**Question 1: The adiabatic enthalpy drop across the prime mover of the Rankine cycle is 750 kJ/kg. The enthalpy of steam supplied is 2250 kJ/kg. If the back pressure is 0.1 bar and the corresponding hf from the tables is 300 kJ/kg, determine the thermal efficiency.**

Answer - The net work can be found by estimating heat rejected in condensor, Q_{L} and from first law, net work equals net heat transfer (Van Wylen p 287).

Heat lost in condensor per kg = 300kJ/kg + pressure work = 300 +v_{3}*(1-.1)*10^{5}J/kg

From Tables V_{3} = .001, so pressure work =.0009 KJ/kg which can be neglected. Efficiency is Eta= Wn/qH = (750 -300)/2250 = .2.

**Question 2: The following equation is one of the cubic equations of state P = RT/(v-b) - a/(v ^{2}+cbv+db^{2}). Rewrite this equation if the gas in consideration is an ideal gas.**

Answer - Given p=RT/(v-b) - a/(v^{2} + cbv +db^{2})

For an ideal gas a, b, c are zero

Hence p = RT/v or pv = RT.

**Question 3: One kg of CO2 has a volume of 1 m ^{3} at 127^{o}C. Compute the pressure by the perfect gas equation.**

Answer - One kg of CO2 has a volume of V at 127 deg C.

By perfect gas eqn. pV = nRT

Since MW of CO2 is 44, no. of moles n= 1/44

p = nRT/V = 1/44 *R*(127+273), R= 8.3143 KJ/kg mol K

p = (400*8.3143*1/44)/V where v in m^{3}/kg

**Question 4: The Clapeyron equation of state provides a relationship between which combination of the following thermodynamic properties?**

**A. Temperature**

**B. Specific volume**

**C. Pressure**

**D. Enthalpy**

**E. Entropy**

Answer - Clapeyron eqn. of state relates T, V, P, h by dp/dT = dh/(TdV)

The quantities involved T, V, p, h

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**Question 5: When the Joule-Thomson coefficient, μ _{JT} is negative during a throttling process, what does it mean regarding temperature change?**

Answer - Joule Thompson coefficient is negative during throttling.

This is not true for all substances, only for those where initial ambient temp. is below the maximum inversion temp. (see derivation of JT coeff.)

JT coeff = (dT/dP) at const h

If positive, the temp rises on throttling, if negative it drops.

**Question 6: The four Maxwell relations for simple compressible mass provide relationships between which combination of the following thermodynamic properties?**

**A. Temperature**

**B. Specific volume**

**C. Pressure**

**D. Enthalpy**

**E. Entropy**

Answer - The 4 Maxwell relations provide relations for p, v. T, s

**Question 7: As p tends to zero at fixed T, the compressibility factor tends to what?**

Answer - Compressibility Z is defined as PV/RT

If p → 0, then Z - → 0, assuming T does not change.

**Question 8: Which of the following statements is true of the expression pv/ZT if Z is the compressibility factor, T is the temperature, v- is the specific volume and p is pressure.**

**A. It is specific for every gas.**

**B. It is the same for all gases only when pressure is zero.**

**C. It is different for all gases all the time.**

**D. It is the same for all gases at all conditions.**

Answer - Z = pV/RT defines the non ideality of the gas.

It varies with the gas and conditions, being 0 for p=0, Hence A, B, C are true.

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