To determine which temperature represents the highest average kinetic energy of the particles in a sample, we need to compare the given temperatures. Here are the steps:
1. Identify and Convert Temperatures to Kelvin (K) if needed:
- (1) [tex]\( 298 \, \text{K} \)[/tex]
- (3) [tex]\( 27^{\circ} \text{C} \)[/tex] can be converted to Kelvin: [tex]\( 27 + 273.15 = 300.15 \, \text{K} \)[/tex]
- (2) [tex]\( 26 \% \, \text{K} \)[/tex] is not a valid temperature.
- (4) [tex]\( 12^{\circ} \text{C} \)[/tex] can be converted to Kelvin: [tex]\( 12 + 273.15 = 285.15 \, \text{K} \)[/tex]
2. List the converted temperatures for easy comparison:
- [tex]\( 298 \, \text{K} \)[/tex]
- [tex]\( 300.15 \, \text{K} \)[/tex]
- [tex]\( 285.15 \, \text{K} \)[/tex]
3. Compare the temperatures:
- [tex]\( 300.15 \, \text{K} \)[/tex] is higher than [tex]\( 298 \, \text{K} \)[/tex]
- [tex]\( 300.15 \, \text{K} \)[/tex] is higher than [tex]\( 285.15 \, \text{K} \)[/tex]
Thus, the highest temperature is [tex]\( 300.15 \, \text{K} \)[/tex], which corresponds to [tex]\( 27^{\circ} \text{C} \)[/tex].
4. Identify the correct answer option:
- Option (3) [tex]\( 27^{\circ} \text{C} \)[/tex].
Therefore, the temperature representing the highest average kinetic energy of the particles in a sample is:
(3) [tex]\( 27^{\circ} \text{C} \)[/tex]
