Given below are two statements :
Statements 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 :
Statements 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)Both statement I and Statement II are true
- (B)Statement I is true but Statement II is false✓ Correct
- (C)Both Statement I and Statement II are false
- (D)Statement I is false but Statement II is true
Answer: (B)
Solution
With and , and since , the speeds stand in the ratio , so the root-mean-square speed indeed doubles and the first statement holds. For the second, an ideal gas obeys while the translational kinetic energy is , so is only two-thirds of that energy, not equal to it. The first statement is true and the second is false.
JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Single correct option