Excess Pressure Inside a Liquid Drop and Soap Bubble
Physics · Mechanical Properties Of Fluids · NEET
The curved surface of a liquid pulls inward, so the pressure inside is higher than outside. A liquid drop has one surface, so excess pressure = 2T/r. A soap bubble has two surfaces (inner and outer), so excess pressure = 4T/r. An air bubble inside a liquid has one surface again, so 2T/r. Memory hook: "bubble in air has 2 skins, so 4; drop and bubble-in-water have 1 skin, so 2."
A liquid drop and an air bubble in water each have one surface (excess pressure 2T/r), while a soap bubble in air has two surfaces (excess pressure 4T/r). Always count surfaces first.
Your doubts, answered
Why is the excess pressure in a soap bubble 4T/r but in a liquid drop only 2T/r?
A liquid drop (like a rain drop) is solid liquid inside with only ONE surface touching air. So excess pressure = 2T/r. A soap bubble is a thin film with air inside AND air outside, so it has TWO surfaces (inner and outer), each contributing 2T/r. Total = 2T/r + 2T/r = 4T/r. Count the surfaces first, then multiply.
What about an air bubble inside water? Is it 2T/r or 4T/r?
An air bubble inside a liquid has only ONE surface (the water-air boundary around it). So its excess pressure is 2T/r, same as a liquid drop. Only the soap bubble in air has two surfaces. NCERT states this clearly: a bubble of gas in a liquid uses 2S/r, a bubble of liquid in gas (soap bubble) uses 4S/r.
Does the excess pressure depend on how much liquid or air is inside?
No. It depends only on surface tension T and radius r, through 2T/r or 4T/r. A smaller radius gives a LARGER excess pressure. That is why a small bubble has higher inside pressure than a big bubble, and why you must blow hard to start a small bubble.
When a soap bubble expands (r gets bigger), what happens to the pressure inside?
Excess pressure = 4T/r. As r increases, 4T/r decreases, so the pressure inside DROPS. This is a direct NEET 2022 question. Bigger bubble = smaller inside pressure.
How do I connect excess pressure to depth in water?
Excess pressure is a real pressure in pascals. If a question says the inside pressure equals the pressure at depth Z below water, set 4T/r = rho g Z (for a soap bubble). Solve for Z. This is exactly the NEET 2019 numerical below.
⚠️ The NEET trap ✗ Using 4T/r for an air bubble rising inside water, because it 'looks like a bubble'. ✓ An air bubble in water has only ONE surface, so use 2T/r. The 4T/r formula is ONLY for a soap bubble in air, which has two liquid surfaces. 🧠 Ask 'how many liquid surfaces?' Two surfaces means 4, one surface means 2. The word 'bubble' alone does not decide it.
Real NEET questions
NEET 2019
A soap bubble of radius 1 mm is blown from a detergent solution of surface tension 2.5 x 10^-2 N/m. The pressure inside the bubble equals the pressure at a point Z0 below the free surface of water in a container. Taking g = 10 m/s^2 and density of water = 10^3 kg/m^3, the value of Z0 is:
A · 100 cm
B · 10 cm
C · 1 cm ✓
D · 0.5 cm
Solution: Soap bubble has two surfaces, so excess pressure = 4T/r. Substitute T = 2.5 x 10^-2 N/m and r = 1 mm = 10^-3 m. Excess pressure = 4 x 2.5 x 10^-2 / 10^-3 = 0.1 / 10^-3 = 100 Pa. This equals the water gauge pressure rho g Z0. So 100 = 10^3 x 10 x Z0. Therefore Z0 = 100 / 10^4 = 0.01 m = 1 cm. Answer C.
NEET 2022
If a soap bubble expands, the pressure inside the bubble:
A · decreases ✓
B · increases
C · remains the same
D · is equal to the atmospheric pressure
Solution: Excess pressure inside a soap bubble = 4T/r. When the bubble expands, r increases. Since 4T/r is inversely proportional to r, a larger r gives a smaller excess pressure. So the pressure inside decreases. Answer A.
Solved Mechanical Properties Of Fluids NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the formula for excess pressure inside a liquid drop?
Excess pressure = 2T/r, where T is surface tension and r is the radius of the drop. A drop has only one surface.
What is the formula for excess pressure inside a soap bubble?
Excess pressure = 4T/r. A soap bubble has two surfaces (inner and outer), each giving 2T/r, so the total is 4T/r.
What is the excess pressure inside an air bubble in a liquid?
It is 2T/r, because an air bubble inside a liquid has only one surface, just like a liquid drop.
Why is the inside pressure higher than the outside?
The curved liquid surface has surface tension that pulls inward. To balance this inward pull, the pressure inside must be higher than outside by 2T/r or 4T/r.
Which bubble has more pressure inside, a small one or a big one?
The smaller bubble. Since excess pressure = 4T/r, a smaller radius gives a larger pressure. This is why, when two bubbles join, air flows from the small one into the big one.
What are the units of excess pressure here?
Pascals (Pa) or N/m^2. T is in N/m and r is in metres, so 2T/r or 4T/r comes out in N/m^2.
