a)
The amount of heat required for the process.
a)
Answer to Problem 91RP
The amount of heat required for the process is
Explanation of Solution
Write the energy balance equation for the reported process.
Here, input energy is
Write the expression to obtain the amount of heat required for the process
Here, number of moles is N, internal energy of the system at state 1 is
Write the expression to obtain the internal energy of the system at state 1
Here, enthalpy of the system at state 1 is
Write the expression to obtain the internal energy of the system at state 2
Here, enthalpy of the system at state 2 is
Write the expression to obtain the change in enthalpy of the system
Conclusion:
Substitute
Refer Table A-2c, “Ideal-gas specific heats of various common gases”, obtain the specific heat relation as
Substitute
Here, constants are a, b, c and d.
Refer Table A-2c, “Ideal-gas specific heats of various common gases”, obtain the values of constants a, b, c and d for methane as 19.89,
Substitute 19.89 for a,
Substitute
Thus, the amount of heat required for the process is
b)
The amount of heat required for the process.
b)
Answer to Problem 91RP
The amount of heat required for the process is
Explanation of Solution
Write the stoichiometric reaction for the dissociation process.
From the stoichiometric reaction, infer that the stoichiometric coefficient for methane
Write the expression to obtain the actual reaction for the dissociation process.
From the actual reaction, infer that the equilibrium composition contains x amount of methane
Write the expression to obtain the total number of moles
Here, number of moles of
Write the expression to obtain the equilibrium constant
Here, pressure is P.
Write the expression to obtain the mole fraction of Methane
Write the expression to obtain the mole fraction of carbon
Write the expression to obtain the mole fraction of hydrogen
Write the expression to obtain the amount of heat required for the process
Here, specific heat of methane is
Conclusion:
Write the carbon balance equation from Equation (VIII).
Write the hydrogen balance equation from Equation (VIII).
Substitute x for
Substitute
Substitute 0.641 for x in equation (XV).
Substitute 0.641 for x in equation (XVI).
Substitute 0.641 for x in equation (XVII).
Substitute 0.641 for x, 0.359 for y, and 0.718 for z in Equation (VIII).
Substitute 0.641 for x, and 1.718 for
Substitute 0.359 for x, and 1.718 for
Substitute 0.718 for x, and 1.718 for
Substitute 10 kmol for N, 0.37 for
Thus, the amount of heat required for the process is
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Chapter 16 Solutions
Thermodynamics: An Engineering Approach
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