We calculate potential of mean force (PMF) between the spherical particles in an ionic liquid by using an integral equation theory, a statistical mechanical theory for liquids. The PMFs between like-charged particles, unlike-charged particles, charged-uncharged particles, and uncharged particles are calculated. Effect of the particle diameter on the PMF is also studied. It is found that the pairs of the like charged particles, unlike charged particles, and uncharged particles are stabilized when they are closely coupled, whereas the charged-uncharged particles are destabilized by the contact. To investigate roles of the energy and entropy in the PMF, it is decomposed into the energetic and entropic components by a temperature differentiation. It is found that the energetic component has relatively high dependency on the surface charges of the immersed particles. On the other hand, the entropic component does not change much upon change in the surface charges of the immersed particles. Generally, an interaction between two particles in an ionic liquid is often explained by the electrostatic and van der Waals interactions, which are classified as the energetic component. However, we found that the entropic component also plays an important role in the interaction.