(a) The molar mass of oxygen is "M(O_2) = 2 \\cdot M(O) = 2 \\cdot 16 = 32" g/mol. To find the amount of substance we need to divide mass by molar mass
"n = \\frac{m}{M}=\\frac{12}{32}=0.375" mol.
(b) The gas is heated at constant pressure. By definition, "C_p = (\\frac{\\delta Q}{dT})_P". Also, we know that "C_P = \\frac{i+2}{2}R", where i is a number of degrees of freedom, R is universal gas constant. i = 5 (3 translation + 2 rotation, molecules do not vibrate). For n moles of substance we obtain
"\\Delta Q = n \\cdot C_P \\Delta T = \\frac{7}{2} nR \\Delta T = 3.5 \\cdot 0.375 \\cdot 8.314 \\cdot 100= 1091" J.
(c) Assuming we have an ideal gas, "dU = nC_VdT" , "C_V = \\frac{i}{2}R" .
"\\Delta U = \\frac{5}{2}nR\\Delta T"
"\\frac{\\Delta U}{\\Delta Q} = \\frac{\\frac{5}{2}nR\\Delta T}{\\frac{7}{2}nR\\Delta T} = \\frac{5}{7}"
"\\frac{5}{7}" of the heat is used to increase the internal energy of the oxygen.
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