Question:
The temperature at which the mean kinetic energy of the molecules of gas is \(\left(\frac{1}{4}\right)^{th}\) of the mean kinetic energy of its molecules at \(147^{\circ }\text{C}\) is
The temperature at which the mean kinetic energy of the molecules of gas is \(\left(\frac{1}{4}\right)^{th}\) of the mean kinetic energy of its molecules at \(147^{\circ }\text{C}\) is
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Mean kinetic energy is proportional to absolute temperature.
Updated On: Nov 12, 2026
- \(105\) K
- \(-147\) K
- \(173^{\circ }\text{C}\)
- \(-105^{\circ }\text{C}\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
Mean kinetic energy per molecule \(=\dfrac{3}{2}k_BT\), so it is proportional to the absolute temperature.
Step 2: Initial temperature
\(147^{\circ}\text{C}=147+273=420\) K.
Step 3: Calculation
For one-fourth of the energy, \(T'=\dfrac{420}{4}=105\) K.
Final Answer:
The required temperature is 105 K. \[ \boxed{\text{(A) }105\ \text{K}} \]
Mean kinetic energy per molecule \(=\dfrac{3}{2}k_BT\), so it is proportional to the absolute temperature.
Step 2: Initial temperature
\(147^{\circ}\text{C}=147+273=420\) K.
Step 3: Calculation
For one-fourth of the energy, \(T'=\dfrac{420}{4}=105\) K.
Final Answer:
The required temperature is 105 K. \[ \boxed{\text{(A) }105\ \text{K}} \]
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