A hot, freshly-sterilised fermentation medium is cooled in a double-pipe heat-exchanger. The medium enters the inner pipe of the exchanger at 95 \(^\circ C\) and leaves the exchanger at 40 \(^\circ C\). Cooling water, flowing counter-currently to the medium, enters the annulus of the exchanger at 15 \(^\circ C\) and leaves the exchanger at 45 \(^\circ C\). The overall heat transfer coefficient is 1350 W m\(^{-2}\) °C\(^{-1}\). The rate of heat transfer per unit area will be _________ W/m². (Round off to the nearest integer)
In a fermentation process, each mole of glucose is converted to biomass (CH\(_1.8\)O\(_0.5\)N\(_0.2\)), with a biomass yield coefficient of 0.4 C-mol/C-mol, according to the unbalanced equation given below. \[ {C}_6{H}_{12}{O}_6 + {NH}_3 + {O}_2 \to {CH}_1.8{O}_0.5{N}_0.2 + {CO}_2 + {H}_2{O} \] The moles of oxygen consumption per mole of glucose consumed during fermentation is _. (Round off to two decimal places)
The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop. The opamp runs from \( \pm 15 \, {V} \) supplies. If a \( +1 \, {V} \) signal is applied at the input, the output voltage (rounded off to one decimal place) is:
A wheel of mass \( 4M \) and radius \( R \) is made of a thin uniform distribution of mass \( 3M \) at the rim and a point mass \( M \) at the center. The spokes of the wheel are massless. The center of mass of the wheel is connected to a horizontal massless rod of length \( 2R \), with one end fixed at \( O \), as shown in the figure. The wheel rolls without slipping on horizontal ground with angular speed \( \Omega \). If \( \vec{L} \) is the total angular momentum of the wheel about \( O \), then the magnitude \( \left| \frac{d\vec{L}}{dt} \right| = N(MR^2 \Omega^2) \). The value of \( N \) (in integer) is:
In the transistor circuit shown in the figure, \( V_{BE} = 0.7 \, {V} \) and \( \beta_{DC} = 400 \). The value of the base current in \( \mu A \) (rounded off to one decimal place) is: