List of top Process Calculations and Thermodynamics Questions

Consider a vapour-liquid mixture of components A and B that obeys Raoult's law. The vapour pressure of A is half that of B. The vapour phase concentrations of A and B are 3 mol m\(^{-3}\) and 6 mol m\(^{-3}\), respectively. At equilibrium, the ratio of the liquid phase concentration of A to that of B is:

An isolated system consists of two perfectly sealed cuboidal compartments A and B separated by a movable rigid wall of cross-sectional area 0.1 m\(^2\) as shown in the figure. Initially, the movable wall is held in place by latches L1 and L2 such that the volume of compartment A is 0.1 m\(^3\). Compartment A contains a monoatomic ideal gas at 5 bar and 400 K. Compartment B is perfectly evacuated and contains a massless Hookean spring of force constant 0.3 N m\(^{-1}\) at its equilibrium length (stored elastic energy is zero). The latches L1 and L2 are released, the wall moves to the right by 0.2 m, where it is held at the new position by latches L3 and L4. Assume all the walls and latches are massless. The final equilibrium temperature of the gas in compartment A, in K, rounded off to 1 decimal place, is ______.

Heat is available at a rate of 2 kW from a thermal reservoir at 400 K. A two-stage process harnesses this heat to produce power. Stages 1 and 2 reject heat at 360 K and 300 K, respectively. Stage 2 is driven by the heat rejected by Stage 1. If the overall process efficiency is 50% of the corresponding Carnot efficiency, the power delivered by the process, in kW, rounded off to 2 decimal places, is ____.

Ethylene obeys the truncated virial equation-of-state \( \frac{PV}{RT} = 1 + \frac{BP}{RT} \) where \( P \) is the pressure, \( V \) is the molar volume, \( T \) is the absolute temperature, and \( B \) is the second virial coefficient. The universal gas constant \( R = 83.14 \) bar cm\(^3\) mol\(^{-1}\) K\(^{-1}\). At 340 K, the slope of the compressibility factor (\( Z \)) vs. pressure curve is \( -3.538 \times 10^{-3} \) bar\(^{-1}\). Let \( G_R \) denote the molar residual Gibbs free energy. At these conditions, the value of \( \left( \frac{\partial G_R}{\partial P} \right)_T \), in cm\(^3\) mol\(^{-1}\), rounded off to 1 decimal place, is _____.

The Newton-Raphson method is used to solve \( f(x) = 0 \), where \( f(x) = e^x - 5x \). Starting with an initial guess \( x^{(0)} = 1.0 \), the value of the next iterate \( x^{(1)} \), rounded off to 2 decimal places, is _____

Consider a binary mixture of components A and B at temperature \( T \) and pressure \( P \). Let \( \vec{V}_A \) and \( \vec{V}_B \) be the partial molar volumes of A and B, respectively. At a certain mole fraction of A, \( X_A \):
\[ \left( \frac{\partial \vec{V}_A}{\partial X_A} \right)_{T,P} = 22 \text{ cm}^3 \text{ mol}^{-1} \quad \text{and} \quad \left( \frac{\partial \vec{V}_B}{\partial X_A} \right)_{T,P} = -18 \text{ cm}^3 \text{ mol}^{-1} \]
The value of \( X_A \), rounded off to 2 decimal places, is ____.