Final answer:
To find the new temperature of an ideal gas after the removal of thermal energy, calculate the number of moles from the number of atoms, apply the first law of thermodynamics adjusted for a closed system, and use the relation between internal energy and temperature to find the temperature change. After that, convert the final temperature from Kelvin to Celsius.
Step-by-step explanation:
To determine the new temperature of an ideal gas after having thermal energy removed, we can use the first law of thermodynamics, which in a closed system is expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. However, since no work is done we can simplify the relationship to ΔU = Q. For an ideal gas, the change in internal energy (ΔU) can be related to the change in temperature (ΔT) by ΔU = nCvΔT, where n is the number of moles of the gas and Cv is the molar heat capacity at constant volume. Assuming the gas is monatomic, we use Cv = (3/2)R, where R is the ideal gas constant (8.314 J/mol·K).
Firstly we need to calculate the number of moles (n) from the given number of atoms using Avogadro's number (6.022 × 10·23 atoms/mol): n = (2.2 × 10·22 atoms) / (6.022 × 10·23 atoms/mol). After finding n, we can rearrange the equation ΔU = nCvΔT to find ΔT = Q/(nCv). Since 4.3 J of energy is removed Q is -4.3 J (it is negative because energy is removed). The initial temperature, T1, is 20°C, which is 293.15 K. By finding ΔT we can then find the final temperature T2 by T2 = T1 + ΔT.
Finally, to return the result in degrees Celsius, we can convert the final temperature from Kelvin back to Celsius by subtracting 273.15 from T2 in Kelvin.