To determine the change in internal energy of the gas during the compression process, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). In this case, since the gas is being compressed, we need to consider the work done on the gas as negative.
Understanding the Variables
In this scenario, we have the following information:
- Initial volume (V1) = 0.4 m³
- Final volume (V2) = 0.2 m³
- Pressure (P) = 0.105 MPa (which is constant throughout the process)
- Heat transfer (Q) = -42.5 kJ (since heat is leaving the system, we consider it negative)
Calculating Work Done on the Gas
The work done on the gas during a constant pressure process can be calculated using the formula:
W = P × ΔV
Where ΔV is the change in volume, calculated as:
ΔV = V2 - V1 = 0.2 m³ - 0.4 m³ = -0.2 m³
Now, converting the pressure from MPa to kPa for consistency:
P = 0.105 MPa = 105 kPa
Now we can calculate the work done:
W = 105 kPa × (-0.2 m³) = -21 kJ
Applying the First Law of Thermodynamics
Now that we have both the heat transfer and the work done, we can apply the first law:
ΔU = Q - W
Substituting the values we have:
ΔU = -42.5 kJ - (-21 kJ)
ΔU = -42.5 kJ + 21 kJ = -21.5 kJ
Final Result
The change in internal energy of the gas during this compression process is -21.5 kJ. This negative value indicates that the internal energy of the gas has decreased, which is consistent with the heat being removed from the system during compression.
