Chemical Engineering Thermodynamics: First and second Law problems

1.   100 mol of an ideal gas is compressed isothermally at 400 K from 100 kPa to 500 kPa. The process is irreversible and requires 20% more work than for reversible compression. Calculate the entropy change of the gas, entropy change of the surrounding and universe. The surrounding is at 300K.   
Sol: W =  nRTln(P2/P1)
ΔSsys   =  nRln(P2/P1)
 Qsurr  =   1.2xW
 ΔSsurr  =  Qsurr/T(300)
ΔSuniv = ΔSsys + ΔSsurr

2.   A copper rod is of length 1 m and diameter 0.01 m. One end of the rod is at 100°C and, the other at 20°C. The rod is perfectly insulated along its length and the thermal conductivity of copper is 380 W/mK. Calculate the rate of entropy production due to irreversibility of this heat transfer.   
Sol: Q= -kAdT/dx (as heat is transferred axially)
       ΔS = Q[1/293-1/373]  as heat is being transferred from high temperature to low temperature) 

3.   A rigid tank of volume 1 m³ contains 200 moles of CO₂ at 25°C. Electric current of 5 A at 440 V passes through a resistor, placed inside the tank, for 15 min. Determine the final state of CO₂ in the tank. CO₂ may be treated as a vander Waal gas with constants a = 363.077 × 10^-3 Pa (m³/mol)² and b = 0.043 × 10^-3 m³/mol. The change in internal energy of CO₂ can be expressed as 

     dU = c_v dT + dV, with c_v = 32.34 J/molK. 
Sol: dU = dQ + dW
      nc_v dT = V.I.t  
      Find T2 and  calculate P2 using vander Waal equation of state.
 

4.  0.3 m³ of water at 1 bar and 20% quality is enclosed between a cylinder and a piston resting on stops 1 (initial state) as shown in figure. The atmospheric pressure and the weight of piston are such that a pressure of 3 bar is required to lift the piston. The system is heated until the piston reaches the upper stops 2 (final state) where the volume is 0.45 m³. Heating is continued further until water exists as saturated vapour. Show the processes on T-V diagram and determine the final pressure of water, overall heat transfer, work done and entropy change for the process.           
     Sol: intially v = 0.2m(vg) + 0.8m(vl)
           calculate m and get final specific volume as v/m
           find saturation pressure from steam table.
           W = -PextdV
            Find ΔU from initial and final conditions and then calculate q as ΔU-W
            similarly find ΔS