Energy in Thermal physics Please show all steps and units Wh

Energy in Thermal physics: Please show all steps and units:

What is the thermal energy of 1 L of ideal gas at \"standard temperature and pressure\" (0°C, 100,000 Pa)?

What is the thermal energy of 1 L of ideal gas at \"normal temperature and pressure\" (20°C, 101,325 Pa)?

Solution

from ideal gas equation:

                PV = nRT

          (100,000)(1*10^-3) = n(8.314)(0+273)

number of moles = n = 0.044 mol

number of atoms:

     N = nN_A = (0.044)(6.02X10²³) = 2.65X10²² atoms

thermal energy: E = (3/2)NkT = (3/2)(2.65X10²² )(1.38x10^-23)(273) = 149.8 J

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from ideal gas equation:

                PV = nRT

          (101,325)(1*10^-3) = n(8.314)(20+273)

number of moles = n = 0.0416 mol

thermal energy: E = (3/2)nRT = (3/2)(0.0416)(8.314)(293) =151.9875 J = 152 J