Respuesta :
Answer : The change in internal energy and change in enthalpy of the gas is 1143.2 J/mol and 1600.5 J/mol respectively.
Explanation :
(a) The formula used for change in internal energy of the gas is:
[tex]\Delta U=C_v\Delta T\\\\\Delta U=C_v(T_2-T_1)[/tex]
where,
[tex]\Delta U[/tex] = change in internal energy = ?
[tex]C_v[/tex] = heat capacity at constant volume = [tex]20.785J/mol.K[/tex]
[tex]T_1[/tex] = initial temperature = [tex]5^oC=273+5=278K[/tex]
[tex]T_2[/tex] = final temperature = [tex]60^oC=273+60=333K[/tex]
Now put all the given values in the above formula, we get:
[tex]\Delta U=nC_v(T_2-T_1)[/tex]
[tex]\Delta U=(20.785J/mol.K)\times (333-278)K[/tex]
[tex]\Delta U=1143.175J/mol\approx 1143.2J/mol[/tex]
The change in internal energy of the gas is 1143.2 J/mol.
(b) The formula used for change in enthalpy of the gas is:
[tex]\Delta H=C_p\Delta T\\\\\Delta H=C_p(T_2-T_1)[/tex]
where,
[tex]\Delta H[/tex] = change in enthalpy = ?
[tex]C_p[/tex] = heat capacity at constant pressure = [tex]29.100J/mol.K[/tex]
[tex]T_1[/tex] = initial temperature = [tex]5^oC=273+5=278K[/tex]
[tex]T_2[/tex] = final temperature = [tex]60^oC=273+60=333K[/tex]
Now put all the given values in the above formula, we get:
[tex]\Delta U=nC_v(T_2-T_1)[/tex]
[tex]\Delta U=(29.100J/mol.K)\times (333-278)K[/tex]
[tex]\Delta U=1600.5J/mol[/tex]
The change in enthalpy of the gas is 1600.5 J/mol.
