Question

How would you calculate `DeltaE` of a gas for a process in which the gas absorbs 35 J of heat and does 8 J of work by expanding?

Answer 1

This is asking you to apply the first law of thermodynamics:

`stackrel("otherwise known as")stackrel(DeltaU)overbrace(\mathbf(DeltaE))\mathbf( = q + w)`

where:

• `DeltaE` is the change in internal energy.
• `q` is the heat flow in the thermodynamic process.
• `w` is the expansion/compression work performed by the gas or on the gas.

Since the work is done by the gas (rather than on the gas) through the expansion, `w < 0`. Work is also defined as:

`w = -PDeltaV = -P(V_2 - V_1)`

where final volume `V_2` is larger than initial volume `V_1` in an expansion, i.e. when work is negatively-signed. If work were to be positively-signed, then `V_2` would be smaller than `V_1`.

Since the gas absorbs heat, heat flows into the gas, i.e. `q > 0`.

Therefore:

`color(blue)(DeltaE) = ("35 J") + (-"8 J")`

`=` `color(blue)("27 J"`