A long cylindrical pipe of radius 20 ,cm is c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the initial pressure of the air inside be $p_0$ (atmospheric pressure) and initial volume be $V_i$. When a mass $m$ is attached to the piston,

Vedclass · Accepted Answer

$0.04$

Vedclass · Answer

(C) Let the initial pressure of the air inside be $p_0$ (atmospheric pressure) and initial volume be $V_i$. When a mass $m$ is attached to the piston,the piston moves down and the pressure of the gas becomes $p_f = p_0 - \frac{mg}{A}$,where $A$ is the cross-sectional area of the pipe.Since the temperature remains constant during this expansion,we use Boyle's Law: $p_i V_i = p_f V_f$.$p_0 V_i = (p_0 - \frac{mg}{A}) V_f$$\frac{V_f}{V_i} = \frac{p_0}{p_0 - \frac{mg}{A}} = \frac{1}{1 - \frac{mg}{p_0 A}}$Using the binomial approximation $(1-x)^{-1} \approx 1+x$ for small $x = \frac{mg}{p_0 A}$,we get $\frac{V_f}{V_i} \approx 1 + \frac{mg}{p_0 A}$.Thus,$\frac{\Delta V}{V_i} = \frac{V_f - V_i}{V_i} = \frac{mg}{p_0 A}$.When the gas is cooled from $T$ to $T-\Delta T$,it returns to its original volume $V_i$. For a constant pressure process (isobaric),$\frac{V}{T} = 	ext{constant}$,so $\frac{\Delta V}{V_f} = \frac{\Delta T}{T}$.Therefore,$\frac{\Delta T}{T} = \frac{\Delta V}{V_f} \approx \frac{\Delta V}{V_i} = \frac{mg}{p_0 A}$.Given $m = 50 \,kg$,$g = 10 \,m/s^2$,$p_0 = 10^5 \,Pa$,and $r = 0.2 \,m$ $(A = \pi r^2 = 3.14 	imes 0.04 = 0.1256 \,m^2)$:$\frac{\Delta T}{T} = \frac{50 	imes 10}{10^5 	imes 0.1256} = \frac{500}{12560} \approx 0.0398 \approx 0.04$.

Similar Questions

One mole of a perfect gas in a cylinder fitted with a piston has a pressure $P,$ volume $V,$ and temperature $T.$ If the temperature is increased by $1 \, K$ keeping pressure constant,the increase in volume is

At absolute zero temperature,the pressure of an ideal gas will be

An ideal gas is heated from $27^{\circ}C$ to $627^{\circ}C$ at constant pressure. If initial volume of gas is $4 \text{ m}^3$, then the new volume of the gas will be (in $\text{ m}^3$)

To double the volume of a given mass of an ideal gas at $27^{\circ}C$ keeping the pressure constant,one must raise the temperature in degrees Celsius to ....... $^{\circ}C$.

For an ideal gas with pressure $P$,temperature $T$,and volume $V$,where the mass of each molecule is $m$,what is the density of the gas? ($k$ is the Boltzmann constant)

Vedclass Test Series

Exam Paper Generator

Online Exam Module