Answer: The final temperature when heat in the amount of 800 kJ is added to 10 moles of ethylene initially at [tex]200^{o}C[/tex] is [tex]1529.63^{o}C[/tex].
Explanation:
It is known that the heat capacity of ethylene is 2.145 J/g K. Hence, for 10 moles of ethylene its mass will be as follows.
No. of moles = [tex]\frac{\text{mass}}{\text{molar mass}}[/tex]
10 mol = [tex]\frac{\text{mass}}{28.05 g/mol}[/tex]
mass = 280.5 g
Now, we know that relation between heat energy, mass and specific heat is as follows.
q = [tex]mC \times \Delta T[/tex]
[tex]800 \times 10^{3} J = 280.5 \times 2.145 J/g K \times (T - 473) K[/tex]
[tex]800 \times 10^{3} J = 601.67 \times (T - 473) K[/tex]
1329.63 = T - 473
T = 1802.63 K
or, = [tex](1802.63 - 273)^{o}C[/tex]
= [tex]1529.63^{o}C[/tex]
Thus, we can conclude that the final temperature when heat in the amount of 800 kJ is added to 10 moles of ethylene initially at [tex]200^{o}C[/tex] is [tex]1529.63^{o}C[/tex].
