Final answer:
The heat supplied to 2 moles of a diatomic gas, where 50% of the gas molecules are dissociated without a temperature rise, is (11/2)RT. The energy is used for the endothermic dissociation reaction instead of increasing the internal kinetic energy of the gas.
Step-by-step explanation:
The question deals with a scenario where 2 moles of a diatomic gas are subjected to a process where 50% of the molecules get dissociated without an increase in temperature. In thermodynamics, the dissociation of a gas can absorb energy (heat) without changing the temperature through a process known as an endothermic reaction. The energy absorbed is used to break the chemical bonds rather than increasing the kinetic energy of the molecules, which would raise the temperature.
For diatomic gases, such as Hydrogen, Nitrogen, or Oxygen, the internal energy is mainly a function of temperature. The internal energy (U) can be described by the formula U = (5/2)nRT for a diatomic gas at room temperature, where n is the number of moles, R is the ideal gas constant, and T is the temperature. However, in this specific heat problem, there is a complication due to the dissociation of the gas which causes an increase in the number of moles of the gas.
To solve the problem, we must understand that the molar heat capacity at constant volume for a diatomic gas is (5/2)R. Since half of the gas is dissociated, we effectively create another mole of atoms, leading to 3 moles of monatomic gas. Monatomic gas has a molar heat capacity of (3/2)R, which results in the total heat absorbed being the sum of the heat capacities multiplied by the temperature and the number of moles.
The heat supplied therefore is 2*(5/2)RT + 1*(3/2)RT = (5RT + 3RT/2) = (11/2)RT, considering the dissociation process. This is because of the conservation of energy, where the energy supplied goes solely into breaking intermolecular bonds rather than increasing temperature.