Practice free Kinetic Theory of Gases (Physics) NEET multiple-choice questions online with instant answers and detailed explanations. No login required.
For a gas $ { R \over C_v } = 0.67 $ .This gas is made up of molecules which are
$C_v = { R \over 0.67 } = 1.5 R = {3 \over 2 } R $ This is the value for mono atomic gases
The specific heat of an ideal gas is
According to the equilibrium theorem, the molar heat capacities should be independent of temperature How ever, variations in $C_v$ and $C_p$ are observed as the temperature changes. At very high temperatures, vibrations are also inportant and that affects the values of $C_v$ and $C_p$ for diatomic and poly atomic gases. Here in the question according to given information (D) may be correct answer.
The specific heats at constant pressure is greater than that of the same gas at constant volume because
At constant pressure, the gas does work in expanding against the external pressure. This work requires additional energy, which is why the specific heat at constant pressure (C_p) is greater than the specific heat at constant volume (C_v).
One mole of ideal monoatomic gas $ \left( \gamma = {5 \over 3 } \right) $ is mixed with one mole of diatomic gas $ \left( \gamma = {7 \over 3 } \right) $ What is $\gamma $ for the mixture? $\gamma $ denotes the ratio of specific heat at constant pressure to that at constant volume
$ \gamma _{mix} = { { 1\gamma_1 \over \gamma_1 -1 } + { 2\gamma_2 \over \gamma_2 -1 } \over { 1 \over \gamma_1 - 1 } + {2 \over \gamma_2 -1 } } = { { 1 \times 5/3 \over ( 5/3 - 1 ) } + { 1 \times 7/5 \over 7/5 - 1 } \over {1 \over (5/3 -1)} + {1 \over ( 7/5 -1 ) } }= { 3 \over 2} = 1.5 $
For a gas if ratio of specific heats at constant pressure and volume is $ \gamma $, then value of degrees of freedom is
$ \gamma = 1 + { 2 \over f } \Rightarrow \gamma -1 = { 2 \over f } \Rightarrow { f \over 2} = { 1 \over \gamma -1 } $ $ \therefore f = { 2 \over \gamma - 1 } $
The molar specific heat at constant pressure of an ideal gas is The ratio of specific heat at constant pressure to that ratio at constant volume is
molar specific heat at constant pressure, $C_p = 7 \over 2 R $ Since $ C_p - C_v = R \Rightarrow C_v = C_p - R = { 7 \over 2} R -R = { 5 \over 2 } R $
For a gas $ \left( \gamma = {7 \over 5 } \right) $ , the gas may probably be
$ \gamma = 7/5 $ for a diatomic gas
Direction:- Assertion : 300 cc of a gas at $ 27^\circ C$ is cooled at $ -3 ^\circ C$ at constant pressure. The final volume of the gas would be 270 cc Reason : This is as per charle's law $ { V_2 \over V_1 } = { T_2 \over T_1} $
Direction:- Assertion : The time of collision of molecules is of the order of $10^{-8} s $, which is very very small compared to the time between two successive collisions. Reason : This is an experimental fact.
The time of collision of molecules being of the order of \( 10^{-8} \text{ s} \\) is an experimental fact, and it is true. This time is very small compared to the time between two successive collisions. Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion.
Direction:- Assertion : Mean free path of gas varies inversly as density of the gas. Reason : Mean free path varies inversely as pressure of the gas.
The mean free path (\
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