Question

Statement I- The kinetic energy per molecule of the gas is equal to \(\frac{3}{2}k_{B}T\).
\(\{k_{B}\) = Boltzmann constant, T = absolute temperature of the gas\(\}\)
Statement II- For the ideal gas with total energy E, the product \(PV=\left(\frac{3}{2}\right)E\)
\(\{\)P = pressure of the gas and V = volume of the gas\(\}\)

• A. Both statements are correct.
• B. Both statements are incorrect.
• C. Statement I is incorrect and statement II is correct.
• D. Statement I is correct and statement II is incorrect.

Hint:

Average kinetic energy per molecule is 3/2 kT, but PV equals two thirds of the total translational energy.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Kinetic theory gives pressure \(P=\dfrac{1}{3}\dfrac{N}{V}m\overline{v^{2}}\).

Step 2: Statement I
Average translational kinetic energy per molecule is \(\dfrac{3}{2}k_BT\). Statement I is correct.

Step 3: Statement II
\(PV=\dfrac{1}{3}Nm\overline{v^{2}}=\dfrac{2}{3}E\), where \(E=\dfrac{1}{2}Nm\overline{v^{2}}\) is the total energy of the gas.

Step 4: Result
So \(PV=\dfrac{2}{3}E\), not \(\dfrac{3}{2}E\). Statement II is incorrect. Hence option (D).

Final Answer:
Statement I is correct and statement II is incorrect. \[ \boxed{\text{(D) }\text{Statement I is correct and statement II is incorrect.}} \]