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. \(C_p-C_v=\frac{R}{M^2}\)
1. | \(379\) J | 2. | \(357\) J |
3. | \(457\) J | 4. | \(374\) J |
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 \(500~\text{ms}^{-1}\) in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground:
1. | remains the same because \(500~\text{ms}^{-1}\) 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. |
Which of the following diagrams (figure) depicts ideal gas behaviour?
1. | (a), (c) | 2. | (a), (d) |
3. | (c), (d) | 4. | (a), (b) |
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) |
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 |
1. | mass of the gas |
2. | kinetic energy of the gas |
3. | number of moles of the gas |
4. | number of molecules in the gas |
The process on an ideal gas as shown in the figure given below is:
1. isothermal
2. isobaric
3. isochoric
4. none of these