# A sample of gas at 35degree Celsius and 1 atm occupies a volume of 37.5L. At what temp should the gas be kept, if it required to reduce the volume to 3.0 litre at the same pressure?

Jun 7, 2017

The gas should be kept at -248 degrees C.

#### Explanation:

Use Charles Law. Temperature and Volume are directly related using degrees Kelvin. ( if the pressure and number of molecules are kept constant.

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

${V}_{1} = 37.5 l$
${T}_{1} = 35 + 273 = 308$ degrees K
${V}_{2} = 3.0 l$
 T_2 = unknown

Substituting these numbers into the equation gives

$\frac{37.5}{308} = \frac{3.0}{T} _ 2$ multiplying across gives

${T}_{2} = 308 \times \frac{3.0}{37.5}$ Which gives

T_2 = 24.6 degrees K

Subtract 273 to find degrees C.

$24.6 - 273 = - 248$ degrees C. ( to three significant digits.)