Answer
(a) $365K$
(b) increase
(c) $1.52KJ/K$
(d) $555KJ;555KJ$
Work Step by Step
(a) We can find the required temperature as follows:
$T=\frac{PV}{nR}$
We plug in the known values to obtain:
$T=\frac{(100KPa)(4m^3)}{(132mol)(8.31J/mol.K)}$
$T=0.365\times 10^3K$
$T=365K$
(b) The entropy of the system increases because the heat is added to the system at constant temperature.
(c) We can find the change in entropy as follows:
$\Delta S=\frac{nRTln(\frac{V_f}{V_i})}{T}$
We plug in the known values to obtain:
$\Delta S=(132mol)(8.31J/mol.K)\ln(\frac{4m^3}{1m^3})$
$\Delta S=1.52KJ/K$
(d) We know that
$W=nRT\ln(\frac{V_f}{V_i})$
We plug in the known values to obtain:
$W=(132mol)(365K)(8.31J/mol.K)\ln(\frac{4m^3}{1m^3})$
$W=555KJ$
Now $T.\Delta S=365K\times 1.52KJ/K=555KJ$
