Question

If the average kinetic energy of the molecules in an ideal gas initially at 18°C doubles, what is the final temperature of the gas?a.)9°Cb.)504°C c.)309°Cd.)36°C

Answer 1

ANSWER

c. 309°C

EXPLANATION

The average kinetic energy of the molecules in an ideal gas is proportional to the temperature of the gas,

$KE=k\cdot T$

Where the temperature is measured in Kelvin.

For this problem it is not necessary to specify what is the value of k, we just need to know that it is a constant.

So, if the kinetic energy doubles, so does the temperature (in Kelvin).

The initial temperature of the gas is,

$T_i=18\degree C+273=291\text{ }K$

If the temperature doubles,

$T_f=2T_i=2\cdot291K=582K$

In degrees Celsius this is,

$T_f=582K-273=309\degree C$

Hence, the final temperature of the gas is 309°C.