Answer: 80J
Explanation:
According to the first principle of thermodynamics:
"Energy is not created, nor destroyed, but it is conserved."
Then this priciple (also called Law) relates the work and the transferred heat exchanged in a system through the internal energy [tex]U[/tex], which is neither created nor destroyed, it is only transformed. So, in this especific case of the compressed gas:
[tex]\Delta U=Q+W[/tex] (1)
Where:
[tex]\Delta U[/tex] is the variation in the internal (thermal) energy of the system (the value we want to find)
[tex]Q=-100J[/tex] is the heat transferred out of the gas (that is why it is negative)
[tex]W[/tex] is the work is done on the gas (as the gas is compressed, the work done on the gas must be considered positive )
On the other hand, the work done on the gas is given by:
[tex]W=-P \Delta V[/tex] (2)
Where:
[tex]P=450kPa=450(10)^{3}Pa[/tex] is the constant pressure of the gas
[tex]\Delta V=V_{f}-V_{i}[/tex] is the variation in volume of the gas
In this case the initial volume is [tex]V_{i}=600{cm}^{3}=600(10)^{-6}m^{3}[/tex] and the final volume is [tex]V_{f}=200{cm}^{3}=200(10)^{-6}m^{3}[/tex].
This means:
[tex]\Delta V=200(10)^{-6}m^{3}-600(10)^{-6}m^{3}=-400(10)^{-6}m^{3}[/tex] (3)
Substituting (3) in (2):
[tex]W=-450(10)^{3}Pa(-400(10)^{-6}m^{3})[/tex] (4)
[tex]W=180J[/tex] (5)
Substituting (5) in (1):
[tex]\Delta U=-100J+180J[/tex] (6)
Finally:
[tex]\Delta U=80J[/tex] This is the change in thermal energy in the compression process.
