Question

At what temperature is the kinetic energy of a gas molecule half of its value at 327°C?

A. 13.5° C
B. 150° C
C. 27° C
D. −123° C

Answer 1

Correct option : C. 27° C. The temperature at which the kinetic energy of a gas molecule is half of its value at 327°C is approximately 27°C, which corresponds to halving the temperature in Kelvins and then converting it back to Celsius.

Step-by-step explanation:

The kinetic energy of a gas molecule is directly proportional to its absolute temperature (in Kelvins). We'll use this fact to find out at which temperature the gas molecule's kinetic energy is half of its value at 327°C. Since the kinetic energy is proportional to temperature, if the kinetic energy is halved, the temperature should also be halved.

First, convert 327°C to Kelvin:

• 327°C + 273.15 = 600.15 K

Now, find half of this temperature:

• 600.15 K / 2 = 300.075 K

Finally, convert this temperature back to Celsius:

• 300.075 K - 273.15 = 26.925°C ≈ 27°C

Therefore, the temperature at which the kinetic energy of a gas molecule is half of its value at 327°C is approximately 27°C (Option C).