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Question

According to Charles' Law, the volume of a gas increases or decreases by ____ of its original volume at 0°C for each degree centigrade rise or ____


A

1273

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B

fall in temperature

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Solution

Step 1: State Charles law

It states that “At constant pressure, the volume of a fixed mass of gas is directly proportional to absolute temperature”.

VTV=kT

Where V is the volume of the gas, T is the temperature and k is a constant.

Step 2: Express Charle's law in relational form

At a particular temperature T1, the volume is V1. By the above law,
V1=kT1 ...1

Similarly, at another temperature T2, the volume is V2 and,
V2=kT2 ...2

Dividing 1 by 2,

V1V2=T1T2

Step 3: Consider specific values for the two temperatures

Let T1=0°C=273K and T2=100°C=373K. The temperatures are chosen arbitrarily. Then,

V1V2=373273V1=V21+100273V1=V2+100V2273

We see that for every 100°C rise in temperature, volume increases by a factor of 100273.

So for every 1°C rise in rise in temperature, volume increases by a factor of 100273100=1273.

Similarly, it can be shown that for every 1°C fall in rise in temperature, volume decreases by a factor of 1273.

Therefore, the volume of a gas increases or decreases by 1273 of its original volume at 0°C for each degree centigrade rise or fall in temperature.


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