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The density $\left(\mathrm{\rho }\right)$ versus pressure (P) of a given mass of an ideal gas is shown at two temperatures T₁ and T₂. Then relation between T₁ and T₂ may be 

1. ${\mathrm{T}}_1>{\mathrm{T}}_2$
2. ${\mathrm{T}}_2>{\mathrm{T}}_1$
3. ${\mathrm{T}}_1={\mathrm{T}}_2$
4. All the three are possible

At constant pressure , ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its original volume is (T = absolute temperature of the gas ) is 
1. T²
2. T
3. 1/T
4. 1/T²

The given P-V curve is predicted by 

1. Boyle's law
2. Charle's law
3. Avogadro's law
4. Gay lussac's law

A graph is plotted with PV/T on y-axis and mass of the gas along x-axis for different gases. The graph is 
1. a straight line parallel to x-axis for all the gases
2. a straight line passing through origin with a slope having a constant value for all the gases
3. a straight line passing through origin with a slope having different values for different values for different gases
4. a straight line parallel to y-axis for all the gases

What will be the ratio of number of molecules of a monoatomic and diatomic gas in a vessel, if the ration of their partial pressures is 5:3?
1. 5:1
2. 3:1
3. 5:3
4. 3:5

An ideal gas is found to obey an additional law VP² = constant. The gas is initially at temperature T and volume V. When it expands to a volume 2V, the temperature becomes
1. $\mathrm{T}/\sqrt{2}$
2. 2T
3. $2\mathrm{T}\sqrt{2}$
4. 4T

Gas at pressure P₀ is contained in a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to 
1. $4{\mathrm{P}}_0$
2. $2{\mathrm{P}}_0$
3. ${\mathrm{P}}_0$
4. $\frac{{\mathrm{P}}_0}{2}$

N (<100) molecules of gas have velocities 1,2,3...N km/s respectively. Then ratio of rms speed and average speed is 
1. 1
2. $\frac{\sqrt{\left(2\mathrm{N}+1\right)\left(\mathrm{N}+1\right)}}{6\mathrm{N}}$
3. $\frac{\sqrt{\left(2\mathrm{N}+1\right)\left(\mathrm{N}+1\right)}}{6}$
4. $2\sqrt{\frac{2\mathrm{N}+1}{6\left(\mathrm{N}+1\right)}}$

Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of V_rms of molecules and speed of sound in mixture ?

1. $\sqrt{3/2}$
2. $\sqrt{2}$
3. $\sqrt{2/3}$
4. $\sqrt{3}$

P-V diagram of a diatomic gas is straight line passing through origin. The molar heat capacity of the gas in the process will be
1. 4R
2. 2.5 R
3. 3R
4. $\frac{4\mathrm{R}}{3}$

The maximum attainable temperature of ideal gas in the process $\mathrm{P}={\mathrm{P}}_0-{\mathrm{\alpha V}}^2$ where ${\mathrm{P}}_0$ and $\mathrm{\alpha }$ are +ve constants
1. $\frac{2{\mathrm{P}}_0}{3\mathrm{nR}}{\left(\frac{P_0}{3\alpha }\right)}^{1/2}$
2. $\frac{{\mathrm{P}}_0}{2\mathrm{nR}}{\left(\frac{\mathit{2}{P}_0}{3\alpha }\right)}^{1/2}$
3. $\frac{2\mathrm{nR}}{P_0}{\left(\frac{\mathit{2}{P}_0}{3\alpha }\right)}^{1/2}$
4. $\frac{2{\mathrm{P}}_0}{\mathrm{nR}}{\left(\frac{P_0}{\mathit{2}\alpha }\right)}^{1/2}$

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $\mathrm{\gamma }$. It is moving with speed v and its suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by 
1. $\frac{\left(\mathrm{\gamma }-1\right)}{2\mathrm{\gamma R}}M{v}^{2}K$
2. $\frac{{\mathrm{\gamma Mv}}^2}{2\mathrm{R}}K$
3. $\frac{\left(\mathrm{\gamma }-1\right)}{2\mathrm{R}}M{v}^{2}K$
4. $\frac{\left(\mathrm{\gamma }-1\right)}{2\left(\mathrm{\gamma }+1\right)\mathrm{R}}M{v}^{2}K$

${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$ are specific heats at constant pressure and constant volume respectively. It is observed that 
${\mathrm{C}}_{\mathrm{p}}$ - ${\mathrm{C}}_{\mathrm{v}}$= a for hydrogen gas
${\mathrm{C}}_{\mathrm{p}}$ - ${\mathrm{C}}_{\mathrm{v}}$= b for nitrogen gas 
The correct relation between a and b is :
1. a = 14 b
2. a = 28 b
3. $\mathrm{a}=\frac{1}{14}\mathrm{b}$
4. a = b
 

Work done by a system under isothermal change from a volume V1 to V2 for a gas which obeys Vander Waal's equation $\left(\mathrm{V}-\mathrm{\beta n}\right)\left(P+\frac{\alpha n^2}{V}\right)=nRT$ is 
1. $nRT {\log }_2\left(\frac{{\mathrm{V}}_2-\mathrm{n\beta }}{{\mathrm{V}}_1-\mathrm{n\beta }}\right)+\alpha n^2\left(\frac{V_{\mathit{1}}\mathit{-}{V}_{\mathit{2}}}{V_{\mathit{1}}{V}_{\mathit{2}}}\right)$
2. $nRT {\log }_{10}\left(\frac{{\mathrm{V}}_2-\mathrm{n\beta }}{{\mathrm{V}}_1-\mathrm{n\beta }}\right)+\alpha n^2\left(\frac{V_{\mathit{1}}\mathit{-}{V}_{\mathit{2}}}{V_{\mathit{1}}{V}_{\mathit{2}}}\right)$
3. $nRT {\log }_e\left(\frac{{\mathrm{V}}_2-\mathrm{n\beta }}{{\mathrm{V}}_1-\mathrm{n\beta }}\right)+\alpha n^2\left(\frac{V_{\mathit{1}}\mathit{-}{V}_{\mathit{2}}}{V_{\mathit{1}}{V}_{\mathit{2}}}\right)$
4. $nRT {\log }_e\left(\frac{{\mathrm{V}}_2-\mathrm{n\beta }}{{\mathrm{V}}_1-\mathrm{n\beta }}\right)+\alpha n^2\left(\frac{V_{\mathit{1}}{V}_{\mathit{2}}}{V_{\mathit{1}}\mathit{-}{V}_{\mathit{2}}}\right)$

Consider the shown diagram where the two chambers separated by piston-spring arrangement contain equal amounts of certain ideal gas. Initially when the temperatures of the gas in both the chambers are kept at 300 K. The compressiin in the spring is 1 m. The temperature of the left and the right chambers are now raised to 400 K and 500 K respectively. If the pistons are free to slide, the compression in the spring is about.

1. 1.3 m
2. 1.5 m
3. 1.1 m
4. 1.0 m

An experiment is carried on  afixed amount of gas at different temperatures and at high pressure such that it deviates from the ideal gas behaviour. The variation of $\frac{\mathrm{PV}}{\mathrm{RT}}$ with P is shown in the diagram. The correct variation will correspond to 

1. Curve A
2. Curve B
3. Curve C
4. Curve D

An air bubble of volume v₀ is released by a fish at a depth h in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density of water is $\mathrm{\rho }$)
1. ${\mathrm{v}}_0$
2. ${\mathrm{v}}_0\left(\mathrm{\rho gh}/\mathrm{p}\right)$
3. $\frac{{\mathrm{v}}_0}{\left(1+{\displaystyle \frac{\mathrm{\rho gh}}{\mathrm{p}}}\right)}$
4. ${\mathrm{v}}_0\left(1+\frac{\mathrm{\rho gh}}{\mathrm{p}}\right)$