The conversion of sulfur dioxide \( \text{SO}_2 \) to sulfur trioxide \( \text{SO}_3 \) in the Contact Process is a key step in the production of sulfuric acid. This reaction occurs in the presence of a vanadium(V) oxide catalyst.
Step 1: Reaction Characteristics:
The reaction:
\[ 2\ \text{SO}_2 (g) + \text{O}_2 (g) \rightarrow 2\ \text{SO}_3 (g) \]
is known to be exothermic, releasing heat. The standard enthalpy change \( \Delta H^\circ \) for this reaction is negative, indicating that heat is released to the surroundings.
Step 2: Reversibility:
This reaction is also reversible. Under industrial conditions, it does not go to completion, and the formation of \( \text{SO}_3 \) can be reversed back to \( \text{SO}_2 \) and \( \text{O}_2 \) under certain conditions.
The use of a catalyst and optimized conditions such as temperature and pressure help shift the equilibrium towards the formation of more \( \text{SO}_3 \).
Step 3: Industrial Significance:
The exothermic nature of the reaction helps in maintaining operational efficiency, while its reversibility is critical for maximizing \( \text{SO}_3 \) yield through the recirculation of unreacted gases and careful control of reaction conditions.
A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. The initial temperature (at time $t = 0$) of the hot plate and cold plate are $T_h$ and $T_c$, respectively. Assume perfect contact between the plates. Which one of the following is an appropriate boundary condition at the surface $S$ for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for $t>0$?

The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:

\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is _________ MPa (rounded off to 3 decimal places).
An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity \( k = 0.1 \) W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface __________°C (rounded off to 1 decimal place).

GIVEN:
Kinematic viscosity: \( \nu = 1.0 \times 10^{-6} \, {m}^2/{s} \)
Prandtl number: \( {Pr} = 7.01 \)
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]