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?

1 Answer
Jul 10, 2016

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"