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. \(C_p-C_v=\frac{R}{M^2}\)
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. | \(l\propto \dfrac{1}{d}\) |
To find out the degree of freedom, the correct expression is:
1.
2.
3.
4.
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
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) |
1. | \(\dfrac{3}{2}k_BT\) | 2. | \(\dfrac{5}{2}k_BT\) |
3. | \(\dfrac{7}{2}k_BT\) | 4. | \(\dfrac{1}{2}k_BT\) |
A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ\text{C}.\) 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. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)