JEE Main 2022 · 29 June · morning · Single correct · +4 / −1
In van der Waal equation [ P + a/V² ] [V - b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants a/b is dimensionally equal to :
- (a) P/V
- (b) V/P
- (c) PV
- (d) PV³
Answer and solution
Answer (c) PV
Solution
Physics sir · 3 steps
You can only add like to like: a/V² must be a pressure and b must be a volume.
- Find a. Only quantities with the same dimensions can be added, so a/V² has the dimensions of pressure. That gives [a] = [P][V²] = PV².
- Find b. In the second bracket, b is subtracted from V, so b has the dimensions of volume: [b] = V.
[a/b] = PV²/V = PV
- So. The ratio a/b is dimensionally equal to PV, which is option (c).
The idea to keep. Every term added to or subtracted from a quantity carries that quantity's dimensions. Use this to find the dimensions of any constant inside a bracket.
Answer from the NTA final answer key. Solution by PrepWiser.