86. Nitrogen gas (molecular weight 28) is enclosed in a cylinder by a piston, at the initial condition of 2 bar, 298 K and 1 m³. In a particular process, the gas slowly expands under isothermal condition, until the volume becomes 2 m³. Heat exchange occurs with the atmosphere at 298 K during this process.
    The work interaction for the nitrogen gas is
    

1. 1. 200 kJ
      

   
   
   

   2. 138.6 kJ
      

   
   
   

   3. 2 kJ
      

   
   
   

   4. –200 kJ

   
   
   

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1. View Hint View Answer Discuss in Forum

   Work interaction ,

   
   

   W = cln		V2
   		V1

   
   

   W = P1V1ln		V2
   		V1

   
   W = 2 × 10⁵ × ln(2)
   W = 2 × 10⁵ × 0.693
   W = 1.386 × 10⁵ J = 138.6 kJ

   Correct Option: B

   Work interaction ,

   
   

   W = cln		V2
   		V1

   
   

   W = P1V1ln		V2
   		V1

   
   W = 2 × 10⁵ × ln(2)
   W = 2 × 10⁵ × 0.693
   W = 1.386 × 10⁵ J = 138.6 kJ

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87. A 2 kW, 40 litres water heater is switched on for 20 minutes. The heat capacity cp for water is 4.2 kJ/kgK. Assuming all the electrical energy has gone into heating the water, increase of the water temperature in degree centigrade is
    

1. 1. 2.7
      

   
   
   

   2. 4.0
      

   
   
   

   3. 14.3
      

   
   
   

   4. 25.25

   
   
   

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1. View Hint View Answer Discuss in Forum

   Energy given by water = Energy taken by heater P.t = mc_p ∆T = 2 × 20 × 60 = 40 × 4.2 × ∆t ∆t = 14.3 °C

   Correct Option: C

   Energy given by water = Energy taken by heater P.t = mc_p ∆T = 2 × 20 × 60 = 40 × 4.2 × ∆t ∆t = 14.3 °C

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88. A vertical cylinder with a freely floating piston contains 0.1 kg air at 1.2 bar and a small electrical resistor. The resistor of is wired to an external 12 volt battery. When a current of 1.5 amps is passed through the resistor for 90 secs, the piston sweeps a volume of 0.01 m³. Assume
    (i) piston and the cylinder are insulated and (ii) air behaves as an ideal gas with cv = 700 J/kgK,
    Find the rise in temperature of air.
    

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

   5. not defined

   
   
   

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1. View Hint View Answer Discuss in Forum

   m = 0.1 kg , P = 1.2 bar , Voltage E = 12 volt I = 1.5 A , t = 90 sec ∆v = 0.01/m³ , C_v = 700 J/kg–K
   Insulated condition δq = 0
   δq = δw + ∆U
   0 = mCv∆T + δw_air - δw_e
   

   ∆T =	δwair - δwe
   	mCv

   
   

   ∆T =	1.2 × 105 × 0.01 - 12 × 1.5 × 90
   	0.1 × 700

   Correct Option: E

   m = 0.1 kg , P = 1.2 bar , Voltage E = 12 volt I = 1.5 A , t = 90 sec ∆v = 0.01/m³ , C_v = 700 J/kg–K
   Insulated condition δq = 0
   δq = δw + ∆U
   0 = mCv∆T + δw_air - δw_e
   

   ∆T =	δwair - δwe
   	mCv

   
   

   ∆T =	1.2 × 105 × 0.01 - 12 × 1.5 × 90
   	0.1 × 700

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89. A steel ball of mass 1 kg of specific heat 0.4 kJ/ kgK is at a temperature of 60°C. It is dropped into 1 kg water at 20°C. The final steady state temperature of water is
    

1. 1. 23.5°C
      

   
   
   

   2. 30°C
      

   
   
   

   3. 35°C
      

   
   
   

   4. 40°C
      

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   N/A

   Correct Option: E

   N/A

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90. The first law of thermodynamics takes the form W = –∆H when applied to
    

1. 1. A closed system undergoing a reversible adiabatic process
      

   
   
   

   2. An open system undergoing an adiabatic process with negiigible changes in kinetic and potential energies
      

   
   
   

   3. A closed system undergoing a reversible constant volume process
      

   
   
   

   4. A closed system undergoing a reversible constant pressure process.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Steady flow equation is given be,
   H₁ + q = H₂ + W
   Adiabatic q = 0
   H₁ – H₂ = W
   W = -∆H

   Correct Option: B

   Steady flow equation is given be,
   H₁ + q = H₂ + W
   Adiabatic q = 0
   H₁ – H₂ = W
   W = -∆H

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