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) |
The equation of state for 5g of oxygen at a pressure P and temperature T, when occupying a volume V, will be: (where R is the gas constant)
1. PV = 5 RT
2. PV = (5/2) RT
3. PV = (5/16) RT
4. PV = (5/32) RT
To find out the degree of freedom, the correct expression is:
1.
2.
3.
4.
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. \(C_p-C_v=\frac{R}{M^2}\)
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
The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:
1. \(l\propto \dfrac{1}{d^2}\)
2. \(l\propto d\)
3. \(l\propto d^2 \)
4. \(l\propto \dfrac{1}{d}\)
The temperature at which the rms speed of atoms in neon gas is equal to the rms speed of hydrogen molecules at \(15^{\circ} \mathrm{C}\) is: (Atomic mass of neon \(=20.2\) u, molecular mass of hydrogen \(=2\) u)
1. \(2.9\times10^{3}\) K
2. \(2.9\) K
3. \(0.15\times10^{3}\) K
4. \(0.29\times10^{3}\) K
1. | all vessels contain unequal number of respective molecules. |
2. | the root mean square speed of molecules is same in all the three cases. |
3. | the root mean square speed of helium is the largest. |
4. | the root mean square speed of sulfur hexafluoride is the largest. |
1. | \(223\) \(\text{K}\) | 2. | \(669^\circ \mathrm{C}\) |
3. | \(3295^\circ \mathrm{C}\) | 4. | \(3097\) \(\text{K}\) |