Answer
a) $561.73 \ J$
b) $-466.4 \ J$
c) $93.35 \ J$
d) 17 percent
e) The maximum temperature is 487 Kelvin. The minimum temperature is 405 Kelvin.
Work Step by Step
a) We first find the initial temperature by simplifying the ideal gas law:
$T = \frac{PV}{nR}=\frac{(8\times101.3\times10^3))(1\times10^{-3})}{.2\times8.314}=487 \ K$
Thus, we find the heat absorbed is:
$Q=-W=-(-nRTln(\frac{V_2}{V_1}))$
$Q=nRTln(\frac{V_2}{V_1})$
$Q=(.2)(8.314)(487)ln2=561.73 \ J$
b) We use a similar process, this time considering heat absorbed, to find:
$Q=-nRTln(\frac{V_2}{V_1})$
$Q=-nR(\frac{PV}{nR})ln(\frac{V_2}{V_1})$
$Q=-PVln(\frac{V_2}{V_1})$
$Q=-(2.05\times101.3\times10^3)(3.24\times10^{-3}ln(.5))=-466.4 \ J$
c) We add the answers to a and b to find:
$W=-466.4+561.73=93.35 \ J$
d) $e=\frac{93.35}{561.73 }\times 100=17$%
e) We found in part a that the maximum temperature is 487 Kelvin. The minimum temperature is:
$T = \frac{PV}{nR}=\frac{(2.05\times101.3\times10^3)(3.24\times10^{-3})}{.2\times8.314}=404.64 \ K$
