An ideal gas equation can be written as where and are respectively,
(1) mass density, the mass of the gas
(2) number density, molar mass
(3) mass density, molar mass
(4) number density, the mass of the gas
The fraction of molecular volume to the actual volume occupied by oxygen gas at STP is: (Take the diameter of an oxygen molecule to be 3 Å).
1. 4 × 10−4
2. 5 × 10−4
3. 3 × 10−4
4. 1 × 10−4
The figure shows a plot of \(\dfrac{PV}{T}\) versus \(P\) for \(1.00\times10^{-3} \) kg of oxygen gas at two different temperatures.
Then relation between \(T_1\) and \(T_2\) is:
1. \(T_1=T_2\)
2. \(T_1<T_2\)
3. \(T_1>T_2\)
4. \(T_1 \geq T_2\)
The value of \(\frac{PV}{T}\) where the curves meet on the \(y\)-axis is:
1. \(0.06~\text{JK}^{-1}\)
2. \(0.36~\text{JK}^{-1}\)
3. \(0.16~\text{JK}^{-1}\)
4. \(0.26~\text{JK}^{-1}\)
An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm, and its temperature drops to 17 °C. The mass of oxygen taken out of the cylinder is:
1. 0.14 kg
2. 0.16 kg
3. 0.18 kg
4. 0.21 kg
An air bubble of volume 1.0 rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?
1. 5.3 cm3
2. 4.0 cm3
3. 3.7 cm3
4. 4.9 cm3
What is the total number of air molecules (inclusive of oxygen, nitrogen, water vapor, and other constituents) in a room of capacity \(25.0\) m3 at a temperature of \(27^\circ \text C\) and \(1\) atm pressure?
1. \(6.1\times10^{23}\) molecules
2. \(6.1\times10^{26}\) molecules
3. \(7.1\times10^{23}\) molecules
4. \(7.1\times10^{26}\) molecules
1. | \(11 . 21 \times 10^{- 20}~\text{J}\) | 2. | \(3 . 09 \times 10^{- 16}~\text{J}\) |
3. | \( 6 . 21 \times 10^{- 21} ~\text{J} \) | 4. | \(5 . 97 \times 10^{- 19}~\text{J}\) |
At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the RMS speed of a helium gas atom at \(-20^\circ \text{C}?\)
(Given the atomic mass of \(\mathrm{Ar}=39.9~\text{u}\) and of \(\mathrm{He}=4.0~\text{u}\))
1. \(1.01 \times 10^3 ~\text{K} \)
2. \(3.15 \times 10^3 ~\text{K} \)
3. \(1.91 \times 10^3~ \text{K} \)
4. \(2.52 \times 10^3 ~\text{K}\)