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).
The internal energy of air in $ 4 \, \text{m} \times 4 \, \text{m} \times 3 \, \text{m} $ sized room at 1 atmospheric pressure will be $ \times 10^6 \, \text{J} $. (Consider air as a diatomic molecule)
Bird : Nest :: Bee : __________
Select the correct option to complete the analogy.
A ship of 3300 tonne displacement is undergoing an inclining experiment in seawater of density 1025 kg/m\(^3\). A mass of 6 tonne is displaced transversely by 12 m as shown in the figure. This results in a 0.12 m deflection of a 11 m long pendulum suspended from the centerline. The transverse metacenter of the ship is located at 7.25 m above the keel.
The distance of the center of gravity from the keel is ________ m (rounded off to two decimal places).
