[Four-digit Integer] A vertical cylinder closed from both ends is equipped with an easily moving pis β States of Matter and Gaseous State Chemistry Question
Question
[Four-digit Integer] A vertical cylinder closed from both ends is equipped with an easily moving piston dividing the volume into two parts, each containing one mole of air. In equilibrium at 320 K, the volume of the upper part is 4.0 times greater than that of the lower part. At what temperature (in kelvin) will the ratio of these volumes be equal to 3.0?
![Chemistry diagram for: [Four-digit Integer] A vertical cylinder closed from both ends is equipped with an easily moving piston dividing the vol](https://urywdhpqdpvmqzlenttu.supabase.co/storage/v1/object/public/question-images/nk/ch03_exII_Q5.png)
Answer: 0450
π‘ Solution & Explanation
Piston equilibrium: $T\!\left(\frac{r^2-1}{r}\right)=\text{const}$ where $r=V_{upper}/V_{lower}$. At 320 K, $r=4$: const $=320\times\frac{15}{4}=1200$ K. For $r=3$: $T\times\frac{8}{3}=1200 \Rightarrow T=450$ K. Answer: $\boxed{0450}$
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