Answer :
The value of u for the reaction that releases 10.1 kJ at constant volume and at constant pressure releases 8.4 kJ is -1.7 kJ (option D).
To find the value of u for the given reaction, we are supposed to calculate the internal energy of the reaction. There is a difference in internal energy of a system between constant volume and constant pressure, and this difference can be represented by ΔU = qv – PΔV, where qv is the heat gained by the system at constant volume, and PΔV is the work done by the system at constant pressure.
The change in internal energy is given by ΔU = qv – PΔV. Here, qv = 10.1 kJ (constant volume) and qp = 8.4 kJ (constant pressure). We know that the internal energy is a state function, and hence, its value is independent of the path. Thus,
ΔU = ΔUv + Δn R T = qv + PΔV
Δn R T = ΔU - qv = qp - qv
= 8.4 kJ - 10.1 kJ
= -1.7 kJ
Thus, the value of u for the reaction is -1.7 kJ (Option D).
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The correct answer is option A. The internal energy change (ΔU) for the reaction is calculated using the heat released at constant volume, which is -10.1 kJ.
In thermodynamics, the change in internal energy (ΔU) of a system is the sum of the heat exchanged (q) and the work done (w). At constant volume, no work is done (w = 0), so the heat exchanged equals the change in internal energy (ΔU = qv).
Given:
- At constant volume, the heat released: [tex]q_v = 10.1\ kJ[/tex]
- At constant pressure, the heat released: [tex]q_p = 8.4\ kJ[/tex]
ΔU can therefore be directly equated to the heat released at constant volume:
- [tex]\Delta U = q_v = -10.1\ kJ[/tex]
So, the correct answer is A. -10.1 kJ.
