Question:
Which of the following shows the correct relationship between the pressure \(\mathrm{P}\) and density \(\rho\) of an ideal gas at constant temperature ?
Options (1) to (4) are P versus \(\rho\) graphs.
Which of the following shows the correct relationship between the pressure \(\mathrm{P}\) and density \(\rho\) of an ideal gas at constant temperature ?
Options (1) to (4) are P versus \(\rho\) graphs.
Options (1) to (4) are P versus \(\rho\) graphs.
Show Hint
For an ideal gas \(P = \rho RT/M\), so at constant T pressure is directly proportional to density.
Updated On: Nov 11, 2026
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
For an ideal gas, \(PV = nRT = \frac{m}{M}RT\).
Hence \(P = \frac{m}{V}\frac{RT}{M} = \frac{\rho RT}{M}\).
At constant temperature \(P \propto \rho\), i.e. P versus \(\rho\) is a straight line with positive slope.
Graph (1) is a hyperbola (inverse relation), (2) is a concave curve, (3) is a line of negative slope; only graph (4) is an increasing straight line.
Answer: (4) increasing straight line graph (P rising linearly with \(\rho\))
Hence \(P = \frac{m}{V}\frac{RT}{M} = \frac{\rho RT}{M}\).
At constant temperature \(P \propto \rho\), i.e. P versus \(\rho\) is a straight line with positive slope.
Graph (1) is a hyperbola (inverse relation), (2) is a concave curve, (3) is a line of negative slope; only graph (4) is an increasing straight line.
Answer: (4) increasing straight line graph (P rising linearly with \(\rho\))
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main The Kinetic Theory of Gases Questions
- The temperature of a gas having \( 2.0 \times 10^{25} \) molecules per cubic meter at 1.38 atm (Given, \( k = 1.38 \times 10^{-23} \, \text{JK}^{-1} \)) is:
- The average kinetic energy of a monatomic molecule is 0.414 eV at temperature: (Use \( k_B = 1.38 \times 10^{-23} \, \text{J/mol-K} \))
- The parameter that remains the same for molecules of all gases at a given temperature is :
- The temperature of a gas is \(-78^\circ\text{C}\) and the average translational kinetic energy of its molecules is \( K \). The temperature at which the average translational kinetic energy of the molecules of the same gas becomes \( 2K \) is:
- The speed of sound in oxygen at S.T.P. will be approximately: Given, \( R = 8.3 \, \text{J K}^{-1} \), \( \gamma = 1.4 \))
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions