In this study, we propose an experiment to investigate the possibility of long-distance thermodynamic relationship in quantum thermodynamics. We consider a pair of spin-1 2 particles prepared in an entangled singlet state in which one particle is sent to Alice and the other to her distant mate Bob, who are spatially separated. Our proposed experiment consists of three different setups: First, both particles are coupled to two heat baths with various temperatures. In second setup, only Alice's particle is coupled to a heat bath and finally, in the last setup, only Bob's particle is coupled to a heat bath. We study the evolution of an open quantum system using the first law of thermodynamics based on the concepts of ergotropy, adiabatic work, and operational heat, in a quantum fashion. We analyze and compare ergotropy and heat transfer in three setups. Our results show that the thermodynamic process ocuurring for two entangled particles and their baths are dependent on each other. We prove that the existence of quantum correlations affects the thermodynamic behavior of distant particles in an entangled state.