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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 the translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below.

Asked in JEE Main 24th Jan 1st Shift 2023 · Speed with temperature and molar mass

• (1) Statement I is false but Statement II is true.
• (2) Both Statement I and Statement II are true.
• (3) Both Statement I and Statement II are false.
• (4) Statement I is true but Statement II is false.

Step-by-step solution

Why the other options are wrong

• (1) Reverses both judgements; the speed calculation is the sound one.
• (2) Accepts Statement II, but PV is 2/3 of the translational kinetic energy, not equal to it.
• (3) Rejects Statement I, but 200 K to 800 K is a factor 4 in T and so a factor 2 in speed.

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