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 $(P)$ $\frac{1}{3} n m \bar{v}^{2}$ $(B)$ Pressure exerted by ideal gas $(Q)$ $\sqrt{\frac{3 RT}{M}}$ $(C)$ Average kinetic energy of a molecule $(R)$ $\frac{5}{2} RT$ $(D)$ Total internal energy of $1$ mole of a diatomic gas $(S)$ $\frac{3}{2} k_{B} T$
| Column $- I$ | Column $- II$ |
| $(A)$ Root mean square speed of gas molecules | $(P)$ $\frac{1}{3} n m \bar{v}^{2}$ |
| $(B)$ Pressure exerted by ideal gas | $(Q)$ $\sqrt{\frac{3 RT}{M}}$ |
| $(C)$ Average kinetic energy of a molecule | $(R)$ $\frac{5}{2} RT$ |
| $(D)$ Total internal energy of $1$ mole of a diatomic gas | $(S)$ $\frac{3}{2} k_{B} T$ |
- A$(A) - (R), (B) - (P), (C) - (S), (D) - (Q)$
- B$(A) - (Q), (B) - (R), (C) - (S), (D) - (P)$
- C$(A) - (Q), (B) - (P), (C) - (S), (D) - (R)$
- D$(A) - (R), (B) - (Q), (C) - (P), (D) - (S)$
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Similar Questions
The plot that depicts the behavior of the mean free time $t$ (time between two successive collisions) for the molecules of an ideal gas,as a function of temperature $(T)$,qualitatively,is (Graphs are schematic and not drawn to scale)
Following statements are given:
$(1)$ The average kinetic energy of a gas molecule decreases when the temperature is reduced.
$(2)$ The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
$(3)$ The average kinetic energy of a gas molecule decreases with increase in volume.
$(4)$ Pressure of a gas increases with increase in temperature at constant volume.
$(5)$ The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:
$(1)$ The average kinetic energy of a gas molecule decreases when the temperature is reduced.
$(2)$ The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
$(3)$ The average kinetic energy of a gas molecule decreases with increase in volume.
$(4)$ Pressure of a gas increases with increase in temperature at constant volume.
$(5)$ The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Statement $I$: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$,where $\gamma = C_p/C_v, T_i = $ initial temperature,$T_f = $ final temperature. Statement $II$: Relation between degree of freedom $f$ and $\gamma(= C_p/C_v)$ is $\gamma = 1 + \frac{2}{f}$. Choose the correct answer from the options given below.
$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in the same vessel at temperature $T$. The mean square of the velocity of molecules of gas $B$ is $v^2$ and the mean square of $x$ component of the velocity of molecules of gas $A$ is $w^2$. The ratio $\frac{w^2}{v^2}$ is
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View SolutionSelect the correct statement.
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