JEE Main 2023 · 24 January · morning · Single correct · +4 / −1
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 option given below :
- (a) Statement I is true but Statement II is false
- (b) Both Statement I and Statement II are true
- (c) Statement I is false but Statement II is true
- (d) Both Statement I and Statement II are false
Answer and solution
Answer (a) Statement I is true but Statement II is false
Solution
Physics sir · 4 steps
Convert both temperatures to kelvin first: 200 K to 800 K is a factor of 4, and the square root makes it 2.
- Kelvin first. Gas laws only work with absolute temperature. -73°C = 200 K and 527°C = 800 K, so the temperature becomes 4 times larger.
v₂/v₁ = √(T₂/T₁) = √(800/200) = √4 = 2
- Statement I. Since vᵣₘₛ = √(3RT/M), the rms speed grows as √T. Four times the temperature gives twice the speed, so Statement I is true.
- Statement II. Kinetic theory gives PV = 1/3Nmvᵣₘₛ², while the total translational kinetic energy is E = 1/2Nmvᵣₘₛ². So PV = 2/3E, not E. Statement II is false.
- So. Statement I is true and Statement II is false, which is option (a).
The idea to keep. Always switch to kelvin before taking any temperature ratio. And remember PV = 2/3Eₜᵣₐₙₛ: pressure and translational energy are linked by the factor 2/3.
Answer from the NTA final answer key. Solution by PrepWiser.