To what temperature must a gas sample initally at 13 degrees be raised in order for the avarage energy of its molecules to double?
in general, temperature is related to the average energy (vibration, movement) of molecules. Double the temperature, you double the energy. http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html
so if you were at 13C, or 286K, double that to double average energy. Ans: 576K, or 299C
To determine the temperature at which the average energy of gas molecules doubles, we can use the concept of the average kinetic energy of gas particles, which is related to temperature using the Boltzmann constant.
The average kinetic energy of gas particles can be calculated using the equation:
E_avg = (3/2) * k * T
Where:
E_avg is the average kinetic energy
k is the Boltzmann constant (1.38 × 10^−23 J/K)
T is the temperature in Kelvin
Given that we want to find the temperature at which the average energy doubles, we can set up the following equation:
2 * E_avg = E_avg_initial
Plugging in the values, we have:
2 * (3/2) * k * T_final = (3/2) * k * T_initial
Since the Boltzmann constant and (3/2) are common to both sides of the equation, we can cancel them out:
2 * T_final = T_initial
Simplifying further, we get:
T_final = T_initial / 2
Now, to find the specific temperature at which the average energy doubles, we need to convert the initial temperature from Celsius to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature.
In this case, the initial temperature is 13 degrees Celsius, which can be converted to Kelvin as follows:
T_initial = 13 + 273.15 = 286.15 K
Substituting this value into the equation, we have:
T_final = 286.15 K / 2 = 143.07 K
Therefore, the gas sample must be raised to a temperature of approximately 143.07 Kelvin in order for the average energy of its molecules to double.