Source: Extra Practice
In the Van der Waals equation of state for a real gas, , where is pressure, is volume, is temperature, and is the universal gas constant. What are the dimensions of the constant ?
Options
Option A is correct
Option B
Option C
Option D
Explanation
According to the principle of dimensional homogeneity, terms added or subtracted must have the same dimensions. In the first parenthesis, is added to . Therefore, the dimension of must be the same as the dimension of pressure (). Dimensions of pressure . Dimensions of volume , so has dimensions . Equating the dimensions: .