Question

How do you do this problem.

An ideal gas is slowly compressed at a constant pressure of2.0
atm from 10.0 L to 2.0 L, path B to D in Fig 19-12. If the heatlost
from the gas in the process BD is 2.78 103
J,what is the change in internal energy of the gas?

Answer 1

Complete question:

An ideal gas is slowly compressed at a constant pressure of2.0 atm from 10.0 L to 2.0 L, path B to D in Fig 19-12. If the heat lost from the gas in the process BD is
`2.78*10^(3)\,J` , what is the change in internal energy of the gas?

(The missing figure is attached below)

Answer:

The change in internal energy of the gas is -1158.8 joules

Step-by-step explanation:

To solve this problem we're going to use the first law of thermodynamics, that states the change in the internal energy of a system
`\Delta U` is the sum of the heat
`Q` and the work
`W`:

[tex\Delta U=W+Q [/tex] (1)

The heat lost in BD is
`-2.78*10^(3)\,J` and because it is lost has negative sign, the work is the area under the curve BD that is a rectangle with length
`\Delta V` and height
`P`, using those on (1)

`\DeltaU=P\DeltaV-2.78*10^(3)\,J`

`\DeltaU=(202650\,Pa)(0.008\,m^(3))-2.78*10^(3)\,J`

(8L=0.008
`m^(3)` and 2.0 atm =202650 Pa )

`\DeltaU=-1158.8\,K`

That means internal energy decreses.