In crystal structures, the coordination number refers to the number of nearest neighbors surrounding a central atom or ion. For pure copper, which adopts a face-centered cubic (FCC) crystal structure, the coordination number for an octahedral site is 6. This is because, in the FCC structure, each atom is surrounded by six atoms at an equal distance in an octahedral arrangement.
Step 1: Understanding the options
- Option (A): 4 — This is the coordination number for a tetrahedral site, not an octahedral site.
- Option (B): 6 — Correct. In the FCC structure, the coordination number for an octahedral site is 6.
- Option (C): 8 — This corresponds to the coordination number for a cubic site, which is not correct for the octahedral site in FCC copper.
- Option (D): 12 — This is the coordination number for an atom in a close-packed structure, but not for an octahedral site.
Step 2: Conclusion The correct coordination number for an octahedral site in pure copper is 6, making Option B the correct answer.
Radiative heat flux \( \dot{q} \) at a hot surface at a temperature \( T_s \) can be expressed as \[ \dot{q} = A f(T_s, T_\infty) (T_s - T_\infty) \] where \( A \) is a constant and \( T_\infty \) is the temperature of the surroundings (temperatures are expressed in K). The function \( f(T_s, T_\infty) \) is given by ______.
Match the steel plant related processes in Column I with the associated information in Column II.
Consider the phase diagram of a one-component system given below. \( V_{\alpha} \), \( V_{\beta} \), and \( V_{{Liquid}} \) are the molar volumes of \( \alpha \), \( \beta \), and liquid phases, respectively. Which one of the following statements is TRUE? Given: The change in molar enthalpies, \( \Delta H_{\alpha \to \beta} \) and \( \Delta H_{\beta \to {Liquid}} \), are positive.
For two continuous functions \( M(x, y) \) and \( N(x, y) \), the relation \( M dx + N dy = 0 \) describes an exact differential equation if
A linear regression model was fitted to a set of \( (x, y) \) data. The total sum of squares and sum of squares of error are 1200 and 120, respectively. The coefficient of determination \( R^2 \) of the fit is ......... (rounded off to one decimal place).
Match the phenomena in Column I with the typical observations in Column II.
Consider the gas phase reaction: \[ CO + \frac{1}{2} O_2 \rightleftharpoons CO_2 \] At equilibrium for a particular temperature, the partial pressures of \( CO \), \( O_2 \), and \( CO_2 \) are found to be \( 10^{-6} \, {atm} \), \( 10^{-6} \, {atm} \), and \( 16 \, {atm} \), respectively. The equilibrium constant for the reaction is ......... \( \times 10^{10} \) (rounded off to one decimal place).
For an application where the Reynolds number is to be kept constant, a liquid with a density of 1 g cm\(^-3\) and viscosity of 0.01 Poise results in a characteristic speed of 1 cm s\(^-1\). If this liquid is replaced by another with a density of 1.25 g cm\(^-3\) and viscosity of 0.015 Poise, the characteristic velocity will be ......... cm s\(^-1\) (rounded off to one decimal place).
Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian liquid through a pipe. The maximum velocity in the pipe is proportional to which of the following quantities?
Given: \( \Delta P \) is the difference between the outlet and inlet pressure, \( \mu \) is the dynamic viscosity of the liquid, and \( R \) and \( L \) are the radius and length of the pipe, respectively.