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?

Question

Noah Aldrich · Accepted Answer

You are being asked to use the first law of thermodynamics here:

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

where

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#.

Consequently:

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

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

Axel Alvarado · Answer

undefined To calculate the change in internal energy (ΔE) of a gas, use the first law of thermodynamics equation:

ΔE = Q - W

Where:
ΔE = change in internal energy
Q = heat added to the system
W = work done by the system

Given:
Q = 35 J
W = 8 J

Substitute the values into the equation:

ΔE = 35 J - 8 J
ΔE = 27 J