Which of the following diagrams (figure) depicts ideal gas behaviour?
1. (a), (c)
2. (a), (d)
3. (c), (d)
4. (a), (b)
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground:
1. | remains the same because \(500\) \(\mathrm{ms^{-1}}\) is very much smaller than \(v_{rms}\) of the gas. |
2. | remains the same because the motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls. |
3. | will increase by a factor equal to \(\left(\dfrac{v_{rms}^2+(500)^2}{v_{rms}^2}\right) \)where \(v_{rms}^2\) was the original mean square velocity of the gas. |
4. | will be different on the top wall and bottom wall of the vessel. |
An ideal gas equation can be written as \(P = \dfrac{ρRT}{M_{0}}\) where \(\rho\) and \(M_{0}\) 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
If \(C_p\) and \(C_v\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_p-C_v=R\)
2. \(C_p-C_v=\frac{R}{M}\)
3. \(C_p-C_v=MR\)
4. \(C_p-C_v=\frac{R}{M^2}\)
A cylinder of fixed capacity \(44.8\) litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by \(15.0^\circ~\mathrm{C}?\) (\(R=8.31\) J mol–1 K–1)
1. | \(379\) J | 2. | \(357\) J |
3. | \(457\) J | 4. | \(374\) J |
Match Column I and Column II and choose the correct match from the given choices.
Column I | Column II | ||
(A) | root mean square speed of gas molecules | (P) | \(\dfrac13nm\bar v^2\) |
(B) | the pressure exerted by an ideal gas | (Q) | \( \sqrt{\dfrac{3 R T}{M}} \) |
(C) | the average kinetic energy of a molecule | (R) | \( \dfrac{5}{2} R T \) |
(D) | the total internal energy of \(1\) mole of a diatomic gas | (S) | \(\dfrac32k_BT\) |
(A) | (B) | (C) | (D) | |
1. | (Q) | (P) | (S) | (R) |
2. | (R) | (Q) | (P) | (S) |
3. | (R) | (P) | (S) | (Q) |
4. | (Q) | (R) | (S) | (P) |
A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ~\mathrm{C}.\) Its density is: (\(R=8.3~\text{J mol}^{-1} \text {K}^{-1}\))
1. \(0.2~\text{kg/m}^{3}\)
2. \(0.1~\text{kg/m}^{3}\)
3. \(0.02~\text{kg/m}^{3}\)
4. \(0.5~\text{kg/m}^{3}\)
The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}^2} \)
2. \( \frac{1}{\sqrt{2} n^2 \pi \mathrm{d}^2} \)
3. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)
Which of the following parameters is the same for molecules of all gases at a given temperature?
1. | mass | 2. | speed |
3. | momentum | 4. | kinetic energy |
1. | \(v_a>v_{rms}\) |
2. | \(v_a<v_{rms}\) |
3. | \(v_a=v_{rms}\) |
4. | \(v_{rms}\) is undefined |