The volume of a sample of an ideal gas contracts from `8.4 L` to `4.2 L` as a result of an applied pressure of 1.5 atm. The system also evolved `830 J` of heat during the contraction. Find `Delta U` for this change in state.
Strategy : According to , to find `DeltaU`, we must know `q` an `w`. Since heat flows from system to surrounding, the value of `q` is given as `- 830 J`. The value of `w` can be calculated by

Explanation

`W = - P Delta V`
`= - (1.5 atm) (4.2 L - 8.4 L) (101.3 J L^(-1) atm^(-1))`
`= 638 J`
The sign of `w` is positive because the surrounding do work on the system.
According to
`Delta U = q + w`
`= (-830 J) + (638 J)`
` = - 190 J`