A gas of 1.0 x 10²⁰ atoms or molecules has 1.0 J of thermal energy. Its molar specific heat at constant pressure is 20.8 J/ mol K. What is the temperature of the gas?
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1
Identify the given values: number of atoms (N = 1.0 x 10^20), thermal energy (E = 1.0 J), and molar specific heat at constant pressure (C_p = 20.8 J/mol K).
Calculate the number of moles (n) of the gas using Avogadro's number (N_A = 6.022 x 10^23 atoms/mol). Use the formula n = N / N_A.
Use the formula for thermal energy at constant pressure, E = n * C_p * T, where T is the temperature in Kelvin.
Rearrange the formula to solve for the temperature, T. The formula becomes T = E / (n * C_p).
Substitute the values of E, n, and C_p into the rearranged formula to calculate the temperature T.