Question

$1$ Mole of $C{O}_2$ gas at $300K$ expanded under the reversible adiabatic condition such that its volume becomes $27$ times. The magnitude of work done $\left(inkJ/mol\right)$ is:
(Given $\text{γ}=1.33$ and $C_v=25.10Jmo{l}^{-1}{K}^{-1}forC{O}_2$ )
report your answer by rounding it up to nearest whole number

Answer 1

Answer: 5

Number of moles $=1$
$T_1=300K$
$V_2=27V_1$
$T{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$\left(\frac{T_1}{T_2}\right)={\left(\frac{V_2}{V_1}\right)}^{\gamma -1}$
$T_2=300{\left(\frac{1}{27}\right)}^{\frac{1}{3}}$
$T_2=100K$
Adiabatic condition, $q=0;\Delta E=w=n{C}_v\left(T_2-T_1\right)$
$w=1\times 25.10\left(100-300\right)=-5020J/mole$
$w=-5.02kJ/mole$