IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Shrinking of a Warm Bottle

## Introduction

Pressure, volume and temperature of an ideal gas is given by $$pV=nRT$$. Our air at atmospheric pressure and room temperature and above, very closely follows this relation. This experiment gives a situation to discuss this equation and also throws light on heat transmission through conduction.

## Apparatus

A plastic bottle with a cap, warm water in a pot, funnel.

## Procedure

1. Open the cap and with the help of the funnel, put warm water in the bottle up to about half its height.
2. After a minute or so, remove water from the bottle and put the cap back.
3. See the pattern of shrinking of the bottle as time passes and write your observations.
4. Question: When the cap is put on the bottle after the warm water is removed, is the temperature of air inside less than or greater than that of the bottle wall?
5. Question: Should the air get cooled or warmed as heat is exchanged between the walls and the air?
6. Question: Why does the bottle take a long time in shrinking?

## Discussion

In this experiment, heat exchange takes place between surrounding air, air inside the bottle and the plastic walls. The time scales of these exchanges are different and that should affect the shrinking rate.

Also the air inside will have high humidity, perhaps it will be saturated with vapour. As temperature goes down, some vapour might condense. That will also affect the shrinking pattern.