In a system of ideal gas under constant temperature and volume conditions, the probability of finding a particle in a specific energy state can be determined using the Boltzmann distribution. The Boltzmann distribution gives the probability of a particle being in a specific energy state as a function of the energy of that state, the temperature of the system, and the Boltzmann constant.The probability P E of finding a particle in an energy state E is given by:P E = 1/Z * e^-E/kT where:- E is the energy of the specific state- k is the Boltzmann constant approximately 1.38 10^-23 J/K - T is the temperature of the system in Kelvin- Z is the partition function, which is a normalization factor that ensures the sum of probabilities of all energy states is equal to 1. It is given by the sum of the Boltzmann factors for all possible energy states:Z = e^-E_i/kT where E_i represents the energy of the i-th state.As the overall energy of the system is increased, the probability distribution of particles among the energy states will change. At higher energies, the particles will have a higher probability of being in higher energy states. However, the exact change in the probability of finding a particle in a specific energy state depends on the specific energy levels of the system and the temperature.In general, as the overall energy of the system increases, the Boltzmann distribution will broaden, meaning that particles will be more likely to be found in a wider range of energy states. This is because the increased energy allows the particles to access higher energy states, and the thermal energy kT becomes more significant compared to the energy differences between the states.