Answer :
To determine ΔmU, the change in internal energy, you need to calculate both the heat absorbed and the work done on or by the system. By using the equation for work and given values of volume and pressure, you can calculate the work done by the system. The change in internal energy can then be determined using the first law of thermodynamics. In this case, the change in internal energy is -534.5 kJ.
To determine the change in internal energy (ΔmU) for a system, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat absorbed or released by the system plus the work done on or by the system.
In this case, the system absorbs 65.5 kJ of heat from the surroundings.
To calculate the work done by the system, we can use the equation:
Work = -PΔV
where P is the external pressure and ΔV is the change in volume.
Given the external pressure is 1.00 bar and the change in volume is 18.0 L - 12.0 L = 6.0 L, we can calculate the work:
Work = - (1.00 bar) x (6.0 L) = -6.0 bar.L
Since 1 bar is equivalent to 100 kPa, we can convert the units:
Work = -6.0 bar.L x (100 kPa / 1 bar) = -600 kPa.L
Now we can calculate the change in internal energy (ΔmU):
ΔmU = Q + W = 65.5 kJ + (-600 kPa.L)
ΔmU = 65.5 kJ - 600 kPa.L
Simplifying:
ΔmU = -534.5 kPa.L
Therefore, the change in internal energy is -534.5 kJ.
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