Question

Two moles of an ideal gas are expanded irreversibly and isothermally at ${37}^{\circ }\text{C}$ until the volume is doubled, and 3.41 kJ heat is absorbed from the surroundings.
$\Delta S_{total}\text{(system + surrounding)}$ is $(R=\frac{25}{3}\text{J/molK, ln 2=0.7, ln 3 = 1.1})$:

• A. - 0.667 J/K
• B. 0.667 J/K
• C. 22.7 J/K
• D. 0.0

Answer 1

The correct option is B 0.667 J/K

$\Delta S=\frac{q}{T}$
For surrounding:
$q=-3.41kJ$
$\Delta S=-\frac{3.41\times 1000}{37+273}=-11J{K}^{-1}$
For a process which is irreversible and isothermal:
$\Delta S=C_{v}ln\frac{T_f}{T_i}+nRln\frac{V_f}{V_i}$
$\Delta S=nRln\frac{V_f}{V_i}$
$\Delta S=2\times 8.314ln\frac{2V}{V}=11.667$
$\Delta S_{total}=\Delta S_{system}+\Delta S_{surrounding}$
$=0.667$