Thermodynamics and Thermochemistry 1 Question 28
31. One mole of monoatomic ideal gas expands adiabatically at initial temperature $T$ against a constant external pressure of $1 \mathrm{~atm}$ from $1 \mathrm{~L}$ to $2 \mathrm{~L}$. Find out the final temperature $\left(R=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
$(2005,1 \mathrm{M})$
(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
$$ \begin{gathered} C_{V}\left(T-T_{2}\right)=1(2-1) \text { atm L } \ \Rightarrow \quad T-T_{2}=\frac{1}{C_{V}}=\frac{2}{3 R} \Rightarrow T_{2}=T-\frac{2}{3 \times 0.082} \end{gathered} $$
