What is the change in internal energy (in J) of a system that absorbs 0.523 kJ of heat from its surroundings and has 0.366 kcal of work done on it

The change in internal energy of the system is 2,054 J

Explanation:

The first law of thermodynamics relates the work and the transferred heat exchanged in a system through internal energy. This energy is neither created nor destroyed, it is only transformed.

Taking into account that the internal energy is the sum of all the energies of the particles that the system has, you have:

ΔU= Q + W

where U is the internal energy of the system (isolated), Q is the amount of heat contributed to the system and W is the work done by the system.

By convention, Q is positive if it goes from the environment to the system, or negative otherwise, and W is positive if it is carried out on the system and negative if it is carried out by the system.

In this case:

Replacing:

ΔU= 0.523 kJ + 1.531 kJ

Solving:

ΔU= 2.054 kJ = 2,054 J (being 1 kJ=1,000 J)

The change in internal energy of the system is 2,054 J