List of top General Aptitude Questions asked in GATE Chemical Engineering

Ethylene obeys the truncated virial equation-of-state: \[ \frac{PV}{RT} = 1 + \frac{B}{V}, \] 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 \( R = 83.14 \, \text{bar cm}^3 \text{mol}^{-1}\text{K}^{-1} \). At 340 K, the slope of the compressibility factor vs. pressure curve is \( -3.538 \times 10^{-3} \, \text{bar}^{-1} \). 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 \( \text{cm}^3 \text{mol}^{-1} \), rounded off to 1 decimal place, is:
An isolated system consists of two perfectly sealed cuboidal compartments \( A \) and \( B \) separated by a movable rigid wall of cross-sectional area \( 0.1 \, \text{m}^2 \). Initially, the movable wall is held in place by latches \( L_1 \) and \( L_2 \) such that the volume of compartment \( A \) is \( 0.1 \, \text{m}^3 \). Compartment \( A \) contains a monatomic ideal gas at \( 5 \, \text{bar} \) and \( 400 \, \text{K} \). Compartment \( B \) is perfectly evacuated and contains a massless Hookean spring of force constant \( 0.3 \, \text{N/m} \) at its equilibrium length (stored elastic energy is zero). The latches \( L_1 \) and \( L_2 \) are released, the wall moves to the right by \( 0.2 \, \text{m} \), where it is held at the new position by latches \( L_3 \) and \( L_4 \). Assume all the walls and latches are massless. The final equilibrium temperature, in \( K \), of the gas in compartment \( A \), rounded off to 1 decimal place, is: \includegraphics[width=0.4\linewidth]{q56 CE.PNG}
Heat is available at a rate of \( 2 \, \text{kW} \) from a thermal reservoir at \( 400 \, \text{K} \). A two-stage process harnesses this heat to produce power. Stages 1 and 2 reject heat at \( 360 \, \text{K} \) and \( 300 \, \text{K} \), 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 \( \text{kW} \), rounded off to 2 decimal places, is:
A metallic spherical particle of density \( 7001 \, \text{kg/m}^3 \) and diameter \( 1 \, \text{mm} \) is settling steadily due to gravity in a stagnant gas of density \( 1 \, \text{kg/m}^3 \) and viscosity \( 10^{-5} \, \text{kg m}^{-1} \text{s}^{-1} \). Take \( g = 9.8 \, \text{m/s}^2 \). Assume that the settling occurs in the regime where the drag coefficient \( C_D \) is independent of the Reynolds number, and equals \( 0.44 \). The terminal settling velocity of the particle, in \( \text{m/s} \), rounded off to 2 decimal places, is:
Consider the function \( f(x, y, z) = x^4 + 2y^3 + z^2 \). The directional derivative of the function at the point \( P(-1, -1, -1) \) along \( (\mathbf{i} + \mathbf{j}) \), where \( \mathbf{i} \) and \( \mathbf{j} \) are unit vectors in the \( x \)- and \( y \)-directions, respectively, rounded off to 2 decimal places, is:
Consider the line integral \( \int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r \), with \( \mathbf{F}(\mathbf{r}) = x \mathbf{i} + y \mathbf{j} + z \mathbf{k} \), where \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) are unit vectors in the \( (x, y, z) \) Cartesian coordinate system. The path \( C \) is given by \( \mathbf{r}(t) = \cos(t) \mathbf{i} + \sin(t) \mathbf{j} + t \mathbf{k} \), where \( 0 \leq t \leq \pi \). The value of the integral, rounded off to 2 decimal places, is:}
For the block diagram shown in the figure, the correct expression for the transfer function \( G_d = \frac{y_2(s){d(s)} \) is:} \includegraphics[width=0.7\linewidth]{q48 CE.PNG}
Consider the ordinary differential equation \[ x^2 \frac{d^2y}{dx^2} - x \frac{dy}{dx} - 3y = 0, \] with the boundary conditions \( y(x=1) = 2 \) and \( y(x=2) = 17/2 \). The solution \( y(x) \) at \( x = 3/2 \), rounded off to 2 decimal places, is:
The Newton-Raphson method is used to solve \( f(x) = 0 \), where \( f(x) = e^x - 5x \). If the initial guess \( x^{(0) = 1.0 \), the value of the next iterate, \( x^{(1)} \), rounded off to 2 decimal places, is:}
Alumina particles with an initial moisture content of \( 5 \, \text{kg} \, \text{moisture}/\text{kg dry solid} \) are dried in a batch dryer. For the first two hours, the measured drying rate is constant at \( 2 \, \text{kg} \, \text{m}^{-2} \, \text{h}^{-1} \). Thereafter, in the falling-rate period, the rate decreases linearly with the moisture content. The equilibrium moisture content is \( 0.05 \, \text{kg}/\text{kg dry solid} \), and the drying area of the particles is \( 0.5 \, \text{m}^2/\text{kg dry solid} \). The total drying time, in hours, to reduce the moisture content to half its initial value is:
Let \( r \) and \( \theta \) be the polar coordinates defined by \( x = r \cos\theta \) and \( y = r \sin\theta \). The area of the cardioid \( r = a(1 - \cos\theta) \), \( 0 \leq \theta \leq 2\pi \), is: \includegraphics[width=0.3\linewidth]{q47 CE.PNG}
The temperatures of two large parallel plates of equal emissivity are \( 900 \, \text{K} \) and \( 300 \, \text{K} \). A reflective radiation shield of low emissivity and negligible conductive resistance is placed parallelly between them. The steady-state temperature of the shield, in \( \text{K} \), is:
For the electrolytic cell in a chlor-alkali plant, which of the following statements is/are correct?
Consider a matrix \( A = \begin{bmatrix} -5 & a
-2 & -2 \end{bmatrix} \), where \( a \) is a constant. If the eigenvalues of \( A \) are \( -1 \) and \( -6 \), then the value of \( a \), rounded off to the nearest integer, is \_\_\_\_\_\_\_.
Consider a binary mixture of components \( A \) and \( B \) at temperature \( T \) and pressure \( P \). Let \( \bar{V}_A \) and \( \bar{V}_B \) be the partial molar volumes of \( A \) and \( B \), respectively. At a certain mole fraction of \( A \), \( x_A \): \[ \left( \frac{\partial \bar{V}_A}{\partial x_A} \right)_{T,P} = 22 \, \text{cm}^3 \, \text{mol}^{-1}, \quad \left( \frac{\partial \bar{V}_B}{\partial x_A} \right)_{T,P} = -18 \, \text{cm}^3 \, \text{mol}^{-1}. \] The value of \( x_A \), rounded off to 2 decimal places, is \_\_\_\_\_\_\_.
Which of the following statements with reference to the petroleum/petrochemical industry is/are correct?
If the Prandtl number \( \text{Pr} = 0.01 \), which of the following statements is/are correct?
Consider a linear homogeneous system of equations \( A\mathbf{x} = \mathbf{0} \), where \( A \) is an \( n \times n \) matrix, \( \mathbf{x} \) is an \( n \times 1 \) vector, and \( \mathbf{0} \) is an \( n \times 1 \) null vector. Let \( r \) be the rank of \( A \). For a non-trivial solution to exist, which of the following conditions is/are satisfied?
In an ammonia manufacturing facility, the necessary hydrogen is generated from methane. The facility consists of the following process units: \( P \): Methanator, \( Q \): CO shift convertor, \( R \): CO\(_2\) stripper, \( S \): Reformer, \( T \): Ammonia convertor. The correct order of these units, starting from methane feed, is:
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 \( 3 \, \text{mol} \, \text{m}^{-3} \) and \( 6 \, \text{mol} \, \text{m}^{-3} \), respectively. At equilibrium, the ratio of the liquid phase concentration of \( A \) to that of \( B \) is:
An infinitely long cylindrical water filament of radius \( R \) is surrounded by air. Assume water and air to be static. The pressure outside the filament is \( P_{\text{out}} \) and the pressure inside is \( P_{\text{in}} \). If \( \gamma \) is the surface tension of the water-air interface, then \( P_{\text{in}} - P_{\text{out}} \) is:
The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation (MWh) in a time of 1000 hours (h). The Capacity Factor of a power generation technology is: \[ \text{Capacity Factor} = \frac{\text{Electricity Generation (MWh)}}{\text{Installed Capacity (MW)} \times 1000 \, (\text{h})}. \] Which one of the given technologies has the highest Capacity Factor? \includegraphics[width=0.7\linewidth]{q8 CE.PNG}
In the 4 x 4 array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule. Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals). As per this rule, the maximum number of crosses possible in the empty column is: \includegraphics[width=0.5\linewidth]{q9 CE.PNG}
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be \( 89.85^\circ \), the ratio of the Earth-Sun and Earth-Moon distances is closest to:
A homogeneous azeotropic distillation process separates an azeotropic AB binary feed using a heavy entrainer, \( E \), as shown in the figure. The loss of \( E \) in the two product streams is negligible, so \( E \) circulates around the process in a closed circuit. For a distillation column with fully specified feed(s), given operating pressure, a single distillate stream, and a single bottoms stream, the steady-state degrees of freedom equals 2. For the process in the figure with a fully specified AB feed stream and given column operating pressures, the steady-state degrees of freedom equals: \includegraphics[width=0.5\linewidth]{q14 CE.PNG}