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 $(R=0.0821 $ $L $ $atm$ $ K^{-1}$ $ mol^{-1})$
(2005,1 M)
(a) $T$
(b) $\dfrac{T}{(2)^{5 / 3-1}}$
(c) $T-\dfrac{2}{3 \times 0.082}$
(d) $T+\dfrac{2}{3 \times 0.082}$
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Answer:
Correct Answer: 31. (c)
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=\dfrac{1}{C _V}=\dfrac{2}{3 R} \Rightarrow T _2=T-\dfrac{2}{3 \times 0.082} \end{gathered} $
BETA
