A graph is plotted with PV/T on y-axis and mass of the gas along x-axis for different gases. The graph is

a straight line parallel to x-axis for all the gases
a straight line passing through origin with a slope having a constant value for all the gases
a straight line passing through origin with a slope having different values for different gases
a straight line parallel to y-axis for all the gases

Solution

The molar heat capacities of a mixture of two gases at constant volume is 13 R/6. The ratio of number of moles of the first gas to the second is 1: 2. The respective gases may be

O₂ and N₂
He and Ne
He and N₂
N₂ and He

Solution

A gas mixture consists of 2 moles of oxygen and 4 moles of Argon at temperature T. Neglecting all vibrational moles, the total internal energy of the system is

4 RT
15 RT
9 RT
11 RT

Solution

Work done by a system under isothermal change from a volume V₁ to V₂ for a gas which obeys Vander Waal’s equation \((V-\beta\, n)\left ( p+\frac{\alpha n^{2}}{V} \right )\) is

\(nRTlog_{e}\left ( \frac{V_{2}-n\beta }{V_{1}-n\beta} \right )+\alpha n^{2}\left ( \frac{V_{1}+V_{2}}{V_{1}V_{2}} \right )\)
\(nRTlog_{10}\left ( \frac{V_{2}-n\beta }{V_{1}-n\beta} \right )+\alpha n^{2}\left ( \frac{V_{1}+V_{2}}{V_{1}V_{2}} \right )\)
\(nRTlog_{e}\left ( \frac{V_{2}-n\beta }{V_{1}-n\beta} \right )+\beta n^{2}\left ( \frac{V_{1}+V_{2}}{V_{1}V_{2}} \right )\)
\(nRTlog_{e}\left ( \frac{V_{1}-n\beta }{V_{2}-n\beta} \right )+\alpha n^{2}\left ( \frac{V_{1}V_{2}}{V_{1}+V_{2}} \right )\)

Solution

Air is pumped into an automobile tube upto a pressure of 200 kPa in the morning when the air temperature is 22°C.During the day, temperature rises to 42°C and the tube expands by 2%. The pressure of the air in the tube at this temperature, will be approximately

212 kPa
209 kPa
206 kPa
200 kPa

Solution

If the potential energy of a gas molecule is U = M/r⁶– N/r¹², M and N being positive constants, then the potential energy at equilibrium must be

zero
M²/4N
N²/4M
MN²/4

Solution

Two monatomic ideal gases 1 and 2 of molecular masses m₁ and m₂ respectively are enclosed in separate containers kept at the same temperature.The ratio of the speed of sound in gas 1 to that in gas 2 is given by

\(\sqrt{\frac{m_{1}}{m_{2}}}\)
m_{1}
^m₁⁄_m₂
^m₂⁄_m₁

Solution

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 2 V, the temperature becomes

T/√2
2 T
2 T√2
4 T

Solution

Since VP² = constant,

VP² = 2VP'²

∴ P' = ¹⁄_√2

As ^P⁄_T = constant or T α P,T=thus T becomes T/√2

N molecules, each of mass m,of gas A and 2 N molecules,each of mass 2 m, of gas B are contained in the same vessel which is maintained at a temperature T. The mean square velocity of molecules of B type is denoted by V₂ and the mean square velocity of A type is denoted by V₁, then ^V₁⁄_V₂ is

Solution

Two gases A and B having the same temperature T, same pressure P and same volume V are mixed. If the mixture is at the same temperature T and occupies a volume V,the pressure of the mixture is

Solution

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