What is reversible isothermal expansion?

Question

Naomi Aronson · Accepted Answer

Now, dissect the terms:

Therefore, an infinitely-slow increase in volume at constant temperature is known as a reversible isothermal expansion.

For an ideal gas, whose internal energy #U# is only a function of temperature, we thus have for the first law of thermodynamics:

#DeltaU = q_(rev) + w_(rev) = 0#

Thus, #w_(rev) -= -int PdV = -q_(rev)#, where work is done is from the perspective of the system and #q# is heat flow.

This implies furthermore that...

All the reversible isothermal PV work #w_(rev)# done by an ideal gas to expand was possible by reversibly absorbing heat #q_(rev)# into the ideal gas.

Example of Calculation

Calculate the work performed in a reversible isothermal expansion by #1# #mol# of an ideal gas from #22.7# #L# to #45.4# #L# at #298.15# #K# and a #1# #ba r# initial pressure.

With the ideal gas law, we have that #PV = nRT#, or #P = (nRT)/V#. So, the work is:

#color(green)(w_(rev)) = -int_(V_1)^(V_2) PdV#

#= -int_(V_1)^(V_2) (nRT)/VdV#

#= -nRTlnV_2 - (-nRTlnV_1)#

#= color(green)(-nRTln(V_2/V_1))#,

adverse in terms of the system.

We keep in mind that the pressure did change, but we don't have an idea of how, off-hand. The work thus does not require the use the pressure of #"1 bar"#:

#color(blue)(w_(rev)) = -("1 mol")("8.314472 J/mol"cdot"K")("298.15 K")ln("45.4 L"/"22.7 L")#

#=# #color(blue)(-"1718.3 J")#

(however, one could use the ideal gas law to write #ln(V_2/V_1) = ln(P_1/P_2)# in this constant-temperature situation.)

So, the work involved the ideal gas exerting #"1718.3 J"# of energy to expand, due to the #"1718.3 J"# of heat it absorbed into itself:

#cancel(DeltaU)^(0" for isothermal process") = q_(rev) + w_(rev)#

#=> color(blue)(q_(rev)) = -w_(rev) = color(blue)(+"1718.3 J")#

Olivia Anton · Answer

undefined Reversible isothermal expansion is a process in thermodynamics where a system expands while maintaining a constant temperature. This expansion occurs in such a way that the system absorbs heat from its surroundings to perform work, while the temperature remains constant throughout the process. It is called "reversible" because it can be reversed by compressing the system back to its original state, with the same temperature, without any energy loss.