A spherical soap bubble inside an air chamber at pressure P_0=10^… - Vidyadip

Question

A spherical soap bubble inside an air chamber at pressure $P_0=10^5 Pa$ has a certain radius so that the excess pressure inside the bubble is $\Delta P=144 Pa$. Now, the chamber pressure is reduced to $8 P_0 / 27$ so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure $\Delta P$ in both the cases to be much smaller than the chamber pressure. The new excess pressure $\Delta P$ in $Pa$ is

✓

Answer

(image)

$P - P _0=\Delta P =\frac{4 T }{ R }$

$P =\left( P _0+\frac{4 T }{ R }\right)$

Case-$2$

(image)

$P _1-\frac{8 P _0}{27}=\Delta P _1=\frac{4 T }{ R _1}$

$P _1=\frac{4 T }{ R _1}+\frac{8 P _0}{27}$

Constant temperature process

$PV = P _1 V_1$

$\left( P _0+\frac{4 T }{ R }\right) \frac{4}{3} \pi R ^3=\left(\frac{4 T }{ R _1}+\frac{8 P _0}{27}\right) \frac{4}{3} \pi R _1^3 ;\left(\frac{4 T }{ R }\right),\left(\frac{4 T }{ R _1}\right) \rightarrow \text { (Neglected) }$

$R =\frac{2}{3} R _1 \Rightarrow R _1=\frac{3}{2} R$

$\Delta P _1=\frac{4 T }{ R _1}=\frac{4 T }{3 R } \times 2=\frac{2}{3} \times(144)=96 Pa$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Six vectors, $\overrightarrow a$ through $\overrightarrow f$ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?

Three blocks of masses ${m_1},\,{m_2}$ and ${m_3}$ are connected by massless strings as shown on a frictionless table. They are pulled with a force ${T_3} = 40\,N$. If ${m_1} = 10\,kg,\,{m_2} = 6\,kg$ and ${m_3} = 4\,kg$, the tension ${T_2}$ will be ........ $N$

Relative permeability of iron is $5500,$ then its magnetic susceptibility will be

Which of the following statements is false

The velocity $u$ and displacement $r$ of a body are related as $u^2 = kr$, where $k$ is a constant. What will be the velocity after $1\, second$ ? (Given that the displacement is zero at $t = 0$)

A circular metallic disc of radius $R$ has a small circular cavity of radius $r$ as shown in figure. On heating the system

An electric motor exerts a force of $40 N$ on a cable and pulls it by a distance of $30 m$ in one minute. The power supplied by the motor (in Watts) is

Four masses are joined to a light circular frame as shown in the figure. The radius of gyration of this system about an axis passing through the centre of the circular frame and perpendicular to its plane would be

In the following circuit, bulb rated as $1.5\, V$, $0.45\, W$. If bulbs glows with full intensity then what will be the equivalent resistance between $X$ and $Y$ ............. $\Omega$

Two simple harmonic motion, are represented by the equations ${y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)$

$y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$

Ratio of amplitude of ${y}_{1}$ to ${y}_{2}={x}: 1$. The value of ${x}$ is ...... .