Question

A gas is compressed from 600cm3 to 200cm3 at a constant pressure of 450kPa . At the same time, 100J of heat energy is transferred out of the gas.Part AWhat is the change in thermal energy of the gas during this process?

Answer 1

Answer: 80J

Step-by-step 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
`U`, which is neither created nor destroyed, it is only transformed. So, in this especific case of the compressed gas:

`\Delta U=Q+W` (1)

Where:

`\Delta U` is the variation in the internal (thermal) energy of the system (the value we want to find)

`Q=-100J` is the heat transferred out of the gas (that is why it is negative)

`W` 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:

`W=-P \Delta V` (2)

Where:

`P=450kPa=450(10)^(3)Pa` is the constant pressure of the gas

`\Delta V=V_(f)-V_(i)` is the variation in volume of the gas

In this case the initial volume is
`V_(i)=600{cm}^(3)=600(10)^(-6)m^(3)` and the final volume is
`V_(f)=200{cm}^(3)=200(10)^(-6)m^(3)`.

This means:

`\Delta V=200(10)^(-6)m^(3)-600(10)^(-6)m^(3)=-400(10)^(-6)m^(3)` (3)

Substituting (3) in (2):

`W=-450(10)^(3)Pa(-400(10)^(-6)m^(3))` (4)

`W=180J` (5)

Substituting (5) in (1):

`\Delta U=-100J+180J` (6)

Finally:

`\Delta U=80J` This is the change in thermal energy in the compression process.