Final answer:
The new temperature of the ideal gas after removing 2.9 J of thermal energy can be calculated using the first law of thermodynamics, relating the change in internal energy to heat removed. The number of moles n is found by dividing the given number of atoms by Avogadro's number. The new temperature is then calculated using the formula incorporating the change in energy, the number of moles, and the ideal gas constant.
Step-by-step explanation:
To calculate the new temperature of an ideal gas after thermal energy is removed, we can use the concept of the first law of thermodynamics which relates the change in internal energy, the heat added to the system, and the work done by the system. However, the work done is not provided or relevant in this scenario, so the change in internal energy (ΔU) is equal to the heat removed from or added to the gas (ΔQ).
For a monatomic ideal gas, the change in internal energy can also be expressed as ΔU = (3/2)nRΔT, where n is the amount of substance in moles, R is the ideal gas constant, and ΔT is the change in temperature. Here, however, we don't have the number of moles, but rather the number of atoms. To find n, we can divide the number of atoms by Avogadro's number (6.022×10²23 atoms/mol).
We can rearrange the formula to solve for the new temperature (T2) as follows: T2 = T1 + (ΔQ/(3/2)nR). Substituting the known values, including the conversion of the initial temperature from Celsius to Kelvin, will yield the new temperature of the gas in Kelvin, which can then be converted back to Celsius.