List of top Questions asked in GATE CH

Consider the reaction \( \text{N}_2(g) + 3\text{H_2(g) \rightarrow 2\text{NH}_3(g) \) in a continuous flow reactor under steady-state conditions. The component flow rates at the reactor inlet are: \[ F_{\text{N}_2}^0 = 100 \, \text{mol/s}, \quad F_{\text{H}_2}^0 = 300 \, \text{mol/s}, \quad F_{\text{inert}}^0 = 1 \, \text{mol/s}. \] If the fractional conversion of \( \text{H}_2 \) is \( 0.60 \), the outlet flow rate of \( \text{N}_2 \), in mol/s, rounded off to the nearest integer, is \_\_\_\_\_\_\_.}
Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow of an incompressible Newtonian fluid through a circular pipe of inner radius \( 5.0 \, \text{cm} \). The magnitude of shear stress at the inner wall of the pipe is \( 0.1 \, \text{N} \, \text{m}^{-2} \). At a radial distance of \( 1.0 \, \text{cm} \) from the pipe axis, the magnitude of the shear stress, in \( \text{N} \, \text{m}^{-2} \), rounded off to 3 decimal places, 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 \_\_\_\_\_\_\_.
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 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?
If the Prandtl number \( \text{Pr} = 0.01 \), which of the following statements is/are correct?
Which one of the given statements is correct with reference to gas-liquid contactors for mass transfer applications?
Two parallel first-order liquid phase reactions \( A \xrightarrow{k_1} B \) and \( A \xrightarrow{k_2} C \) are carried out in a well-mixed isothermal batch reactor. The initial concentration of \( A \) in the reactor is \( 1 \, \text{kmol} \, \text{m}^{-3} \), while that of \( B \) and \( C \) is zero. After \( 2 \, \text{hours} \), the concentration of \( A \) reduces to half its initial value, and the concentration of \( B \) is twice that of \( C \). The rate constants \( k_1 \) and \( k_2 \), in \( \text{h}^{-1} \), are respectively:
Consider the block diagram in the figure with control input \( u \), disturbance \( d \), and output \( y \). For the feedforward controller, the ordered pair \( (K, \alpha / \beta) \) is: \includegraphics[width=0.5\linewidth]{q22 CE.PNG}
Consider the control structure for the overhead section of a distillation column shown in the figure. The composition controller (CC) controls the heavy key impurity in the distillate by adjusting the setpoint of the reflux flow controller in a cascade arrangement. The sign of the controller gain for the pressure controller (PC) and that for the composition controller (CC) are, respectively: \includegraphics[width=0.5\linewidth]{q23 CE.PNG}
The velocity field in an incompressible flow is \( \mathbf{v} = axy \, \mathbf{i} + v_y \, \mathbf{j} + \beta \, \mathbf{k} \), where \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) are unit-vectors in the \( (x, y, z) \) Cartesian coordinate system. Given that \( a \) and \( \beta \) are constants, and \( v_y = 0 \) at \( y = 0 \), the correct expression for \( v_y \) is:
The ratio of the activation energy of a chemical reaction to the universal gas constant is \( 1000 \, \text{K} \). The temperature dependence of the reaction rate constant follows the collision theory. The ratio of the rate constant at \( 600 \, \text{K} \) to that at \( 400 \, \text{K} \) 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 rate of a reaction \( A \rightarrow B \) is \( 0.2 \, \text{mol} \, \text{m}^{-3} \, \text{s}^{-1} \) at a particular concentration \( C_{A1} \). The rate constant of the reaction at a given temperature is \( 0.1 \, \text{m}^3 \, \text{mol}^{-1} \, \text{s}^{-1} \). If the reactant concentration is increased to \( 10 \, C_{A1} \) at the same temperature, the reaction rate, in \( \text{mol} \, \text{m}^{-3} \, \text{s}^{-1} \), is:
Consider the steady, uni-directional diffusion of a binary mixture of \( A \) and \( B \) across a vertical slab of dimensions \( 0.2 \, \text{m} \times 0.1 \, \text{m} \times 0.02 \, \text{m} \) as shown in the figure. The total molar concentration of \( A \) and \( B \) is constant at \( 100 \, \text{mol} \, \text{m}^{-3} \). The mole fraction of \( A \) on the left and right faces of the slab are maintained at \( 0.8 \) and \( 0.2 \), respectively. If the binary diffusion coefficient \( D_{AB} = 1 \times 10^{-5} \, \text{m}^2 \, \text{s}^{-1} \), the molar flow rate of \( A \) in \( \text{mol} \, \text{s}^{-1} \), along the horizontal \( x \)-direction is: \includegraphics[width=0.5\linewidth]{q17 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:
The first non-zero term in the Taylor series expansion of \( (1 - x) - e^{-x \) about \( x = 0 \) is:}
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}
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}
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}
Consider the normal probability distribution function \[ f(x) = \frac{4}{\sqrt{2\pi}} e^{-8(x+3)^2}. \] If \( \mu \) and \( \sigma \) are the mean and standard deviation of \( f(x) \) respectively, then the ordered pair \( (\mu, \sigma) \) is:
If \( z_1 = -1 + i \) and \( z_2 = 2i \), where \( i = \sqrt{-1} \), then \( \text{Arg}(z_1 / z_2) \) is:
For positive integers \( p \) and \( q \), with \( \frac{p}{q} \neq 1 \), \[ \left(\frac{p}{q}\right)^{\frac{p}{q}} = \left(\frac{p}{q}\right)^{(p - q)}. \] Then: (1) \( q^p = p^q \)
(2) \( q^p = p^{2q} \)
(3) \( \sqrt{q} = \sqrt{p} \)
(4) \( \sqrt[q]{q} = q\sqrt[p]{p} \)
Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin?