The fact that a heat pump requires energy to move heat from a colder object (the outside of a house) to a hotter object (the inside of the house) is a real life observation of which thermodynamic law?

The correct answer is - the second law of thermodynamics.

Explanation:

The second law of thermodynamics says that the in all heat energy exchange or transfer, and if there is no gain or lose of energy in a system, the potential energy of the particular state in that system will less than that of initial state of the system in any case.

It also suggests that the processes deals with the conversion of the heat energy are irreversible and the energy can be transfer from lower temperature system to higher temperate system without adding energy.

Thus, The fact that a heat pump requires energy to move heat from a colder object to a hotter object is a real life example of the second law of thermodynamics.

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3