Challenge Questions

A reaction A -> B occurs with a first-order rate constant k = 0.05 s−1 at a steady state. The inflow stream contains 2 mol/L of reactant A at a flow rate of 5 L/s. If the reactor is designed to achieve 90% conversion of A, calculate the minimum reactor volume required. 

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Find the Internal Energy at 112 degrees Celsius and 0.65 MPa 
Skill: Bilinear Interpolation


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Part 1: Find the Centroid of the region bounded by the curves y = sinx, y = cosx, x = 0, and x = pi/4. 

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Part 2: Find the volume of the region rotated over the x-axis using the Theorem of Pappus. 

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A hydrocarbon fuel (C₃H₈) is burned in a combustion chamber with excess air. The air is preheated to 400 K, and the combustion products exit at 1800 K. 
Part 1: Calculate the mass of air needed per kg of fuel to maintain a 10% excess air ratio 
Part 2: Find the adiabatic flame temperature assuming complete combustion.

Note: Make sure to include N2 in the Balanced chemical reaction due to its role in the combustion process. 

Answer

Part 1: What is the wavelength in nm of the electromagnetic radiation emitted from the change in energy state of the electron from n = 6 to n = 2. 

Use:
Change in E = (-2.18 x 10^-18J)((1/n(final)^2) + (1/n(initial)^2))

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Part 2: What is the type of electromagnetic radiation that is emitted? If in the visible spectrum, find color. 

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In a chemical reactor, the concentration of a reactant A decreases over time due to a first-order reaction, where the rate of reaction is proportional to the concentration of A. The rate law is given by:
dA/dt = - kA
Where A is the concentration of A (mol/L), k is the rate constant (1/s), and t is time (s).
At time t = 0, the concentration of A is A0.
Question: Determine the concentration of A at any time t. 
Set up a differential equation to complete this task. 

Answer

Power Plant Cycle with Regeneration
A Rankine cycle power plant operates with regeneration using an open feedwater heater (OFWH). Steam enters the turbine at 8 MPa and 500°C and expands isentropically to 0.7 MPa, where some steam is extracted for the OFWH. The remaining steam expands further to the condenser pressure of 10 kPa.
The extracted steam mixes with compressed liquid water from the condenser at the OFWH, ensuring saturated liquid at the heater exit. The water leaving the OFWH is pumped to 8 MPa before entering the boiler.
Given Data:

• Turbine inlet conditions: P1 = 8 MPa, T1 = 500∘C 
• Intermediate pressure for extraction: P2 = 0.7 MPa
• Condenser pressure: P3 = 10 kPa
• Isentropic efficiencies:
  • Turbine: ηT = 85%
  • Pumps: ηP = 85%
• Mass flow rate of steam into the turbine: m˙ = 10 kg/s

1. Determine the mass fraction of steam extracted at 0.7 MPa for regeneration.
   
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