To solve this problem, we use the first law of thermodynamics, which states:
[tex]\[ \Delta U = Q - W \][/tex]
where [tex]\(\Delta U\)[/tex] is the change in internal energy, [tex]\(Q\)[/tex] is the heat absorbed by the system, and [tex]\(W\)[/tex] is the work done by the system.
Firstly, we need to calculate the change in volume ([tex]\(\Delta V\)[/tex]):
[tex]\[ \Delta V = V_{\text{final}} - V_{\text{initial}} \][/tex]
[tex]\[ \Delta V = 0.0006 \, m^3 - 0.0002 \, m^3 \][/tex]
[tex]\[ \Delta V = 0.0004 \, m^3 \][/tex]
Next, we calculate the work done by the gas during the expansion. For an ideal gas expanding at constant pressure, the work done ([tex]\(W\)[/tex]) is given by:
[tex]\[ W = P \Delta V \][/tex]
Substitute the given values for pressure ([tex]\(P = 1.5 \times 10^5 \, Pa\)[/tex]) and [tex]\(\Delta V\)[/tex]:
[tex]\[ W = 1.5 \times 10^5 \, Pa \times 0.0004 \, m^3 \][/tex]
[tex]\[ W = 60 \, J \][/tex]
Now, we apply the first law of thermodynamics. The system absorbs [tex]\(Q = 32 \, J\)[/tex] of heat. Therefore, the change in internal energy ([tex]\(\Delta U\)[/tex]) is:
[tex]\[ \Delta U = Q - W \][/tex]
[tex]\[ \Delta U = 32 \, J - 60 \, J \][/tex]
[tex]\[ \Delta U = -28 \, J \][/tex]
So, the change in internal energy is [tex]\(-28 \, J\)[/tex].
Thus, the correct answer is:
A. [tex]\( -28 \, J \)[/tex]
