What is the ratio of the new volume to the original volume of a gas that cools from 127°C to 27°C under constant pressure?

To find the ratio of the new volume to the original volume of a gas when it cools under constant pressure, we can use Charles's Law. This law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant.

The first step is to convert the temperatures from Celsius to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature.

1. Convert 127°C to Kelvin:

( 127 + 273.15 = 400.15 , K )

2. Convert 27°C to Kelvin:

( 27 + 273.15 = 300.15 , K )

Now, applying Charles's Law:

[

\frac{V_1}{V_2} = \frac{T_1}{T_2}

]

Where:

• ( V_1 ) is the original volume,

• ( V_2 ) is the new volume,

• ( T_1 ) is the initial temperature in Kelvin (400.15 K),

• ( T_2 ) is the final temperature in Kelvin (300.15 K).

Substituting the values into the equation,