Question

Product of $ P $ and $ V $ of an ideal gas related to translational part of internal energy $ E $ as

• A. \( E = P \times V \)
• B. \( E = \frac{P V}{3} \)
• C. \( E = P \times V^2 \)
• D. \( E = \frac{3}{2} P V \)

Hint:

The translational internal energy of an ideal gas is directly related to pressure and volume. The factor \( \frac{3}{2} \) accounts for the degrees of freedom for a monatomic gas.

Answer 1

The Correct Option is B

For an ideal gas, the translational part of the internal energy \( E \) is related to the pressure \( P \) and volume \( V \) by the following equation: \[ E = \frac{3}{2} n k_B T \] where: - \( n \) is the number of moles, - \( k_B \) is the Boltzmann constant, - \( T \) is the temperature. Using the ideal gas law: \[ P V = n R T \] where \( R \) is the gas constant. From this, we get the relationship: \[ E = \frac{3}{2} P V \]
Thus, the correct answer is \( E = \frac{3{2} P V} \).