Thermodynamics and Thermochemistry - Result Question 31
####31. One mole of monoatomic ideal gas expands adiabatically at initial temperature $T$ against a constant external pressure of $1 atm$ from $1 L$ to $2 L$. Find out the final temperature $\left(R=0.0821 L atm K^{-1} mol^{-1}\right)$
$(2005,1 M)$
(a) $T$
(b) $\frac{T}{(2)^{5 / 3-1}}$
(c) $T-\frac{2}{3 \times 0.082}$
(d) $T+\frac{2}{3 \times 0.082}$
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Solution:
- For an irreversible, adiabatic process;
$$ 0=C _V\left(T _2-T _1\right)+p _e\left(V _2-V _1\right) $$
Substituting the values
$$ \begin{gathered} C _V\left(T-T _2\right)=1(2-1) \text { atm L } \ \Rightarrow \quad T-T _2=\frac{1}{C _V}=\frac{2}{3 R} \Rightarrow T _2=T-\frac{2}{3 \times 0.082} \end{gathered} $$
