Given below are two statements :
Statement I : The temperature of a gas is . When the gas is heated to , 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:
Statement I : The temperature of a gas is . When the gas is heated to , 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:
- A.Statement I is true but Statement II is false
- B.Statement I is false but Statement II is true
- C.Both Statement I and Statement II are true
- D.Both Statement I and Statement II are false
Show answer and solution
Correct option: A
Solution
vrms ∝ √T (in Kelvin). T₁ = -73 + 273 = 200 K, T₂ = 527 + 273 = 800 K. The ratio v₂/v₁ = √(800/200) = √4 = 2. So doubling is confirmed → Statement I is TRUE.
For Statement II: the translational KE of n moles is (3/2)nRT = (3/2)PV, not PV itself. So PV equals (2/3) of the translational KE, not equal to it → Statement II is FALSE.
For Statement II: the translational KE of n moles is (3/2)nRT = (3/2)PV, not PV itself. So PV equals (2/3) of the translational KE, not equal to it → Statement II is FALSE.
[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]