71. A vessel of volume 1.0 m³ contains a mixture of liquid water and steam in equilibrium at 1.0 bar. Given that 90% of the volume is occupied by the steam, find the fraction of the mixture. Assume at 1.0 bar, v_f = 0.001 m³/kg and v_g = 1.7 m³/kg.

1. 1. 5.266 × 10^-3

   
   
   

   2. 5.266 × 10³

   
   
   

   3. 3.442 × 10^-3

   
   
   

   4. 3.442 × 10^-7

   
   
   

---

1. View Hint View Answer Discuss in Forum

   v_f = 0.001 m³ /kg
   v_g = 1.7 m³ /kg
   

   mass of mixture =	0.9	+	0.1
   	vg		vf

   
   

   mass of mixture =	0.9	+	0.1	= 100.53 kg
   	1.7		0.001

   
   

   Specific volume v =	1	= 9.947 × 10-3 m3 / kg
   	m

   
   v = v_f + x(v_f - v_g)
   9.947 × 10^-3 = 0.001 + x(1.7 - 0.001)
   x = 5.266 × 10^-3

   Correct Option: A

   v_f = 0.001 m³ /kg
   v_g = 1.7 m³ /kg
   

   mass of mixture =	0.9	+	0.1
   	vg		vf

   
   

   mass of mixture =	0.9	+	0.1	= 100.53 kg
   	1.7		0.001

   
   

   Specific volume v =	1	= 9.947 × 10-3 m3 / kg
   	m

   
   v = v_f + x(v_f - v_g)
   9.947 × 10^-3 = 0.001 + x(1.7 - 0.001)
   x = 5.266 × 10^-3

---

72. At the triple point of a pure substance, the number of degrees of freedom is
    

1. 1. 0
      

   
   
   

   2. 1
      

   
   
   

   3. 2
      

   
   
   

   4. 3

   
   
   

---

1. View Hint View Answer Discuss in Forum

   According to Gibb's phase rule
   P + F = C + 2
   at triple point C = 1, P = 3
   3 + F= 1 + 2
   F = 0

   Correct Option: A

   According to Gibb's phase rule
   P + F = C + 2
   at triple point C = 1, P = 3
   3 + F= 1 + 2
   F = 0

---

---

73. During the phase change of a pure substance
    

1. 1. dG = 0
      

   
   
   

   2. dP = 0
      

   
   
   

   3. dH = 0
      

   
   
   

   4. dU= 0

   
   
   

---

1. View Hint View Answer Discuss in Forum

   dP = 0
   During phase change
   ∆P = 0, ∆T = 0

   Correct Option: B

   dP = 0
   During phase change
   ∆P = 0, ∆T = 0

---

74. Availability of a system at any given state is
    

1. 1. a property of the system
      

   
   
   

   2. the maximum work obtainable as the system goes to dead state
      

   
   
   

   3. the total energy of the system
      

   
   
   

   4. the maximum useful work obtainable as the system goes to dead state
      

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Availability of system of any given state is when no maximum useful work obtainable as the system goes to dead state.

   Correct Option: D

   Availability of system of any given state is when no maximum useful work obtainable as the system goes to dead state.

---

---

75. A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is
    

1. 1. 18000 kJ
      

   
   
   

   2. 9000 kJ
      

   
   
   

   3. 6000 kJ
      

   
   
   

   4. None of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Entropy change for hot reservoir ∆Sh =	Q	=	-9000	= -10 kJ/ k
   	T		900

   
   

   Energy gain in cold reservoir ∆Sc =	Q	=	-9000	= +30 kJ/ k
   	T		300

   
   Loss in availability = T₀[∆S_c + ∆S_h]
   ⇒ Loss in availability = 300(30 – 10) = 300(20) = 6000 kJ

   Correct Option: C

   Entropy change for hot reservoir ∆Sh =	Q	=	-9000	= -10 kJ/ k
   	T		900

   
   

   Energy gain in cold reservoir ∆Sc =	Q	=	-9000	= +30 kJ/ k
   	T		300

   
   Loss in availability = T₀[∆S_c + ∆S_h]
   ⇒ Loss in availability = 300(30 – 10) = 300(20) = 6000 kJ

---