An irreversible gas phase reaction $2 \textbf{P} \rightarrow 4 \textbf{Q} + \textbf{R}$ is conducted in an isothermal and isobaric batch reactor. Assume ideal gas behavior. The feed is an equimolar mixture of the reactant $\textbf{P}$ and an inert gas. After complete conversion of $\textbf{P}$, the fractional change in volume is ________ (round off to $2$ decimal places).
Consider two Carnot engines $C_1$ and $C_2$ as shown in the figure. The efficiencies of the engines $C_1$ and $C_2$ are $0.40$ and $0.35$, respectively. If the temperature of Reservoir $R_1$ is $800 \: K$, then the temperature (in $K$) of Reservoir $R_3$ is ________ (round off to nearest integer).
Consider the following closed loop system with $G_p$ and $G_c$ as the transfer functions of the process and the controller, respectively. For a unit step change in the set point $(y_{sp}$), the change in the value of the response $(y)$ at steady state is _______ (round off to $1$ decimal place).
The decomposition of acetaldehyde $(X)$ to methane and carbon monoxide follows four-step free radical mechanism. The overall rate of decomposition of $X$ is $-r_X=k_2 \bigg( \dfrac{k_1}{2k_3} \bigg) ^{1/2} C_X^{3/2} =k_{\text{overall}}C_X^{3/2}$ where $k_1, k_2$ ... $k_{\text{overall}}$. The activation energy for the overall reaction (in $kJ \: mol^{-1}$) is _______ (round off to nearest integer).
Sum of the eigenvalues of the matrix $\begin{bmatrix} 2 & 4 & 6 \\ 3 & 5 & 9 \\ 12 & 1 & 7 \end{bmatrix}$ is ______ (round off to nearest integer).
A fluid is heated from $40^{\circ}C$ to $60^{\circ} C$ in a countercurrent, double pipe heat exchanger. Hot fluid enters at $100^{\circ}C$ and exits at $70^{\circ}C$. The log mean temperature difference, i.e. LMTD (in $^{\circ}C$), is _____ (round off to $2$ decimal places).
Consider an infinitely long rectangular fin exposed to a surrounding fluid at a constant temperature $T_a=27^{\circ}C$. The steady state one dimensional energy balance on an element of the fin of thickness $dx$ at a distance $x$ ... $^{\circ}C$) at $x=25 \: cm$ is __________ (round off to $1$ decimal place).
Liquid water is pumped at a volumetric flow rate of $0.02 \: m^3 s^{-1}$ from Tank $I$ to Tank $II$, as shown in the figure. Both the tanks are open to the atmosphere. The total frictional head loss for the pipe system is $1.0 \: m$ of water. ... surfaces in the tanks have negligible velocities The power supplied (in $W$) by the pump to lift the water is ________ (round off to $1$ decimal place)
An elementary liquid phase reversible reaction $P \leftrightarrows Q$ is carried out in an ideal continuous stirred tank reactor (CSTR) operated at steady state. The rate of consumption of $P, -r_p$ (in $mol \: \text{litre}^{-1} \text{minute}^{-1}$), is ... reaction mixture is constant throughout the operation. The space time (in minutes) of the CSTR is ______ (round off to $1$ decimal place).
An aqueous suspension at $60^{\circ}C$ is fed to the first effect of a double effect forward feed evaporator with a mass flow rate of $1.25 \: kg \: s^{-1}$ ... $kg$ per $kg$) is ____________ (round off to $2$ decimal places).
A vertically held packed bed has a height of $1 \: m$, and void fraction of $0.1$, when there is no flow through the bed. The incipient (minimum) fluidization is set in by injection of a fluid of density $1 \: kg \: m^{-3}$. The particle density $(\rho_p)$ of the solids ... $9.81 \: m \: s^{-2}$. The pressure drop (in $Pa$) across the height of the bed is ________ (round off to nearest integer).
Two ideal cross-current stages operate to extract $P$ from a feed containing $P$ and $Q$, as shown below. The mass flow rates of $P$ and $Q$ fed to Stage $1$ are $1,000 \: kg h^{-1}$ and $10,000 \: kg \: h^{-1}$, respectively. Pure solvent $(S)$ is ... with the raffinate. The mass flow rate of $P$ (in $kg \: h^{-1}$) in the raffinate from Stage $2$ is ________ (round off to nearest integer)
Consider a vertically falling film of water over an impermeable wall. The film is in contact with a static pool of an non-reactive pure gas. The gas diffuses into the water film over the entire height of the falling film. The height of the film is $1.0 \: m$, and its ... (in $mm \: s^{-1}$), averaged over the entire height of the falling film is __________ (round off to $3$ decimal places)
An exothermic, aqueous phase, irreversible, first order reaction, $Y \rightarrow Z$ is carried out in an ideal continuous stirred tank reactor (CSTR) operated adiabatically at steady state. Rate of consumption of $Y$ (in $\text{ mol litre}^{-1} \text{ minute}^{-1}$ ... of the reactor is $90 \%$, the volume of the CSTR (in $\text{litre}$) is ______ (round off to $2$ decimal places)
The liquid phase irreversible reactions, $P \xrightarrow[]{k_1} Q$ and $P \xrightarrow[]{k_2} R$, are carried out in an ideal continuous stirred tank reactor (CSTR) operating isothermally at steady state. The space time of the CSTR is $1$ minute. Both the reactions are first ... $k_1$ (in minute$^{-1}$) is ______ (correct up to one decimal place)
A catalytic gas phase reaction $P \rightarrow Q$ is conducted in an isothermal packed bed reactor operated at steady state. The reaction is irreversible and second order with respect to the reactant $P$. The feed is pure $P$ with a volumetric flow rate of $1.0$ litre minute $^{-1}$ and ... litre$^2 g_{\text{catalyst}}^{-1}$ mol$^{-1}$ minute$^{-1}$) is _______ (correct up to one decimal place).
Flow of water thorough an equal percentage valve is $900 \text{ litre } h^{-1}$ at $30 \%$ opening, and $1080 \text{ litre } h^{-1}$ at $35 \%$ opening. Assume that the pressure drop across the valve remains constant. The flow rate (in $\text{ litre } h^{-1}$) through the valve at $45\%$ opening is ________ (round off to nearest integer)
Consider the following closed loop system. $G_c, G_f$ , and $G_p$ are the transfer functions of the controller, the final control element and the process, respectively. $Y$ and $Y_{sp}$ are the response and its set point, respectively. For a gain margin of $1.6$, the design value of $K_c$ is __________ (correct up to one decimal place)
Given $\dfrac{dy}{dx}=y-20$, and $y \mid_{x=0}=40$, the value of $y$ at $x=2$ is _________ (round off to nearest integer)
Consider the following dataset. $\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 15 & 25 \\ \hline f(x) & 6 & 8 & 10 & 12 & 5 \\ \hline \end{array}$ The value of the integral $\int _1^{25} f(x) dx$ using Simpson’s $1/3$rd rule is ______ (round off to 1 decimal place)
The product of the eigenvalues of the matrix $\begin{pmatrix} 2 &3 \\ 0& 7 \end{pmatrix}$ is ______________________ (rounded off to one decimal place).
For a hydraulic lift with dimensions shown in figure, assuming $g=10\:m/s^{2}$, the maximum diameter $D_{left}$ (in $m$) that lifts a vehicle of mass $1000 \:kg$ using a force of $100 \:N$ is ____________________ (rounded off to two decimal places).
The liquid flow rate through an equal percentage control valve, when fully open, is $150$ gal/min and the corresponding pressure drop is $50$ psi. If the specific gravity of the liquid is $0.8$, then the valve coefficient, $C_{V}$, in gal/(min $psi^{0.5}$) is _________________ (rounded off to two decimal places).
Consider a sealed rigid bottle containing $CO_{2}$ and $H_{2}O$ at $10$ bar and ambient temperature. Assume that the gas phase in the bottle is pure $CO_{2}$ and follows the ideal gas law. The liquid phase in the bottle contains $CO_{2}$ ... $CO_{2}$ dissolved in $H_{2}O$ is __________________ (rounded off to three decimal places).
If $x,y$ and $z$ are directions in a Cartesian coordinate system and $i$, $j$ and $k$ are the respective unit vectors, the directional derivative of the function $u\left ( x,y,z \right )=x^{2}-3yz$ at the point $\left ( 2,0,-4 \right )$ in the direction $\left ( i+j-2k \right )/\sqrt{6}$_____________ (rounded off to two decimal places).
Two unbiased dice are thrown. Each dice can show any number between $1$ and $6$. The probability that the sum of the outcomes of the two dice is divisible by $4$ is ____________ (rounded off to two decimal places).
The Newton-Raphson method is used to determine the root of the equation $f(x)=e^{-x}-x$. If the initial guess for the root is 0, the estimate of the root after two iterations is _______ (rounded off to three decimal places).
Carbon monoxide $(CO)$ reacts with hydrogen sulphide $(H_2S)$ at a constant temperature of $800\:K$ and a constant pressure of 2 bar as: $CO+H_2S\leftrightharpoons COS+H_2$ The Gibbs free energy of the reaction ${\Delta g^\circ}_{rxn}=22972.3\:J/mol$ and ... only $4\:mol$ of CO are present, the extent of the reaction (in mol) at equilibrium is _________ (rounded off to two decimal places).
For a given binary system at constant temperature and pressure, the molar volume (in $m^{3}$/mol) is given by: $v=30x_{A}+20x_{B}+x_{A}x_{B}\left ( 15x_{A} -7x_{B}\right )$, where $x_{A}$ and $x_{B}$ are the mole fraction of components $A$ and $B$, respectively. The volume change of mixing $\Delta v_{mix}$ (in $m{3}$/mol) at $x_{A}=0.5$ is _______________ (rounded off to one decimal place).
Consider a vessel containing steam at $180^{\circ}C$.The initial steam quality is $0.5$ and the initial volume of the vessel in $1$ $m^{3}$. The vessel loses heat at a constant rate $q$ under isobaric conditions so that the quality of steam reduces to $0.1$ after $10$ ... 21kJ/kg$.}\\ \\ \end{array}$ The rate of heat loss $q$ (in $kJ$/hour) is _____________ (rounded off to the nearest integer).
A fractionator recovers $95$ mol $\%$ $n$-propane as the distillate from an equimolar mixture of $n$-propane and $n$-butane. The condensate is a saturated liquid at $55^{\circ}\:C$ ... Assuming Raoult's law, the condenser pressure (in bar) is _________________ (rounded off to one decimal place).
A centrifugal pump is used to pump water (density $1000$ $kg/m^{3}$) from an inlet pressure of $10^{5}$ $Pa$ to an exit pressure of $2 \times 10^{5}$ $Pa$. The exit is at an elevation of $10$ $m$ ... $g=10$ $m/s^{2}$. Neglecting losses in the system, the power (in Watts) delivered by the pump is __________ (rounded off to the nearest integer).
A solid sphere of radius $1$ $cm$ and initial temperature of $25^{\circ}\:C$ is exposed to a gas stream at $100^{\circ}\:C$. For the solid sphere, the density is $10^{4}$ $kg/m^{3}$ and the specific heat capacity is $500\;J/(kg\:K)$. The density of the gas ... $95^{\circ}\:C$ is ______________ (rounded off to the nearest integer)
Stream $A$ with specific heat capacity $C_{PA}=2000\:J/\left ( kg\:K \right )$ is cooled from $90^{\circ}C$ to $45^{\circ}C$ in a concentric double pipe counter current heat exchanger having a heat transfer area of $8$ $m^{2}$. The cold stream $B$ ... $A$ (in $kg/s$), is _____________________ (rounded off to two decimal places).
A $20$ $cm$ diameter cylindrical solid pellet of a nuclear fuel with density $6000\: kg/m^{3}$ and conductivity of $300\:W/\left ( m\:K \right )$ generates heat by nuclear fission at a spatially uniform rate of $10^{4}\:W/kg$. The heat from ... and azimuthal dependence, the maximum temperature (in $^{\circ}C$) in the pellet at steady state is ________________ (rounded off to the nearest integer).
The elementary, irreversible liquid-phase, parallel reactions, $2A\rightarrow D$ and $2A\rightarrow U$, take place in an isothermal non-ideal reactor. The $C$-curve measured in a tracer experiment is shown in the figure, where $C(t)$ is the ... $2$ mol/Liter. Using the segregated model, the percentage conversion in the reactor is ___________________ (rounded off to the nearest integer)
A first-order irreversible liquid phase reaction $A\rightarrow B\left ( k=0.1\:min^{-1} \right )$ is carried out under isothermal, steady state conditions in the following reactor arrangement comprising an ideal $CSTR$ (Continuous-Stirred Tank Reactor) and two ideal ... From the information in the figure, the volume of the $CSTR$ (in Liters) is ______________ (rounded off to the nearest integer).
The elementary liquid-phase irreversible reactions $A\overset{k_{1}=0.4\: min^{-1}}{\rightarrow}B\overset{k_{2}=0.1\:min^{-1}}{\rightarrow}C$ take place in an isothermal ideal $CSTR$(Continuous-Stirred Tank Reactor). Pure $A$ is fed to the reactor at a ... , is ________________ (rounded off to the nearest integer).
The elementary irreversible gas-phase reaction $A\rightarrow B+C$ is carried out adiabatically in an ideal $CSTR$ (Continuous-Stirred Tank Reactor) operating at 10 $atm$. Pure $A$ enters the $CSTR$ at a flow rate of 10 mol/$s$ and a temperature of $450$ ... referenced to $273 \:K$. The reactor volume (in Liters) for $75\%$conversion is __________________ (rounded off to the nearest integer).