If you have an empty 2.0 L soda bottle at room temperature (22.1 degrees C) what will the new volume be if you put it in your freezer at -4.50 degrees C?

A soda bottle is flexible enough that the volume of the bottle can change even without opening it

1 Answer
Meave60
May 11, 2018

The new volume is #"1.8 L"#.

Explanation:

The soda bottle is not empty. It contains air, which is a gas. According to Charles' law, the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature . This means that if the volume increases, so does the temperature and vice versa. The equation for this law is:

#V_1/T_1=V_2/T_2#

The temperature is given in degrees Celsius, which must be converted to Kelvins by adding #273.15#.

Known

#V_1="2.0 L"#

#T_1="22.1"^@"C + 273.15"="295.3 K"#

#T_2=-4.50^@"C + 273.15"="268.65 K"#

Unknown

#V_2#

Solution

Rearrange the equation to isolate #V_2#. Plug in the known values and solve.

#V_2=(V_1T_2)/T_1#

#V_2=(2.0"L"xx268.65color(red)cancel(color(black)("K")))/(295.3color(red)cancel(color(black)("K")))="1.8 L"# (rounded to two significant figures)

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