Determine whether the following statements are True or False:
$(a)$ "Conduction stops once a rod achieves thermal steady state."
$(b)$ $A$ surface that is a good emitter is also a good absorber.
$(c)$ $A$ perfect black body must be black in color.
$(d)$ The value of heat capacity is the same under different conditions for a given matter.

$(a)$ False. Conduction does not stop; rather, the temperature gradient becomes constant, and the rate of heat transfer remains steady.
$(b)$ True. According to Kirchhoff's law of radiation, for an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.
$(c)$ False. $A$ perfect black body is defined by its ability to absorb all incident radiation, regardless of its appearance or color in the visible spectrum.
$(d)$ False. Heat capacity depends on the state of the matter (e.g., phase) and the conditions under which heat is added (e.g., constant pressure vs. constant volume).