Question

The quantity \( \frac{pV}{kT} \) represents (where \( k \) is the Boltzmann constant)

• A. number of moles of gas.
• B. kinetic energy of gas.
• C. mass of the gas.
• D. number of molecules of gas in one mole.

Hint:

In thermodynamic equations involving gases, \( \frac{pV}{kT} \) gives the number of molecules. If you multiply by Avogadro's number, you get the number of moles.

Answer 1

The Correct Option is D

Step 1: Understanding the equation.
The equation \( \frac{pV}{kT} \) relates pressure \( p \), volume \( V \), temperature \( T \), and the Boltzmann constant \( k \). It is a part of the ideal gas law in terms of molecules. The ideal gas law in molecular form is: \[ pV = NkT \] Where \( N \) is the number of molecules. Therefore, \( \frac{pV}{kT} \) gives the number of molecules of gas in the given volume. Step 2: Conclusion.
Thus, \( \frac{pV}{kT} \) represents the number of molecules of gas in one mole. The correct answer is (D) number of molecules of gas in one mole.