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Given below are two statements : Statement I : The temperature of a gas is −73°C. When the gas is heated to 527°C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below:

1. Both statement I and statement II are true
2. Statement I is false but statement II is true
3. Both statement I and statement II are false
4. Statement I is true but statement II is false

Correct answer: Statement I is true but statement II is false

Solution

Statement I is true because the root mean square speed of gas molecules is proportional to the square root of the absolute temperature, and heating from -73°C to 527°C indeed doubles the speed. Statement II is false as the product of pressure and volume (PV) in an ideal gas relates to work done, not directly to the translational kinetic energy of the molecules.

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