Gas sample has a volume of 0.287 L with an unknown temperature. The same gas has a volume of 0.180 L when the temperature is 37∘C, with no change in the pressure or amount of gas.

What was the initial temperature, in degrees Celsius, of the gas?

205.3°C

Explanation:

Given parameters:

V₁   =  0.287L

V₂ = 0.18L

T₂  = 37°C

Unknown:

T₁  = ?

Solution:

Since we are interested in volume and temperature relationships in a fixed pressure of the balloon, Charles's law will be a perfect solution to this problem.

Charles's law states that "At constant pressure, the volume of a fixed mass of gas is directly proportional to its temperature".

Mathematically;

where V and T are volume and temperature of the gas

              1 and 2 are initial and final states;

let us convert T₂  = 37°C to K;  37 + 273  = 300K

 Input the parameters and solve for the unknown;

               T₁  = 478.3K

Now convert back to °C;    478.3  - 273   = 205.3°C

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