Question:
The translational kinetic energy of the molecules of \(22\) grams of \(CO_2\) at \(27^\circ C\) is
\[
(R=8.314\ \text{J mol}^{-1}\text{K}^{-1})
\]
The translational kinetic energy of the molecules of \(22\) grams of \(CO_2\) at \(27^\circ C\) is
\[
(R=8.314\ \text{J mol}^{-1}\text{K}^{-1})
\]
Show Hint
For any ideal gas,
\[
\text{Total Translational K.E.}
=
\frac32 nRT.
\]
It depends only on the number of moles and absolute temperature, not on the nature of the gas.
Updated On: Jul 29, 2026
- \(1870.6\ \text{J}\)
- \(164.7\ \text{J}\)
- \(2000\ \text{J}\)
- \(2200\ \text{J}\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
The total translational kinetic energy of an ideal gas is
\[
K=\frac{3}{2}nRT,
\]
where
\[
n=\text{number of moles},
\quad
R=\text{universal gas constant},
\quad
T=\text{absolute temperature}.
\]
Step 1: Calculate the number of moles of \(CO_2\). Molar mass of \(CO_2\): \[ M=44\ \text{g mol}^{-1}. \] Given mass, \[ m=22\ \text{g}. \] Hence, \[ n=\frac{m}{M} =\frac{22}{44} =\frac12. \]
Step 2: Convert temperature into Kelvin. \[ T=27^\circ C+273. \] \[ T=300\ K. \]
Step 3: Calculate the translational kinetic energy. \[ K = \frac32 nRT. \] Substituting, \[ K = \frac32 \left(\frac12\right) (8.314)(300). \] \[ K = \frac34(2494.2). \] \[ K = 1870.65\ \text{J}. \] \[ K \approx 1870.6\ \text{J}. \] Therefore, \[ \boxed{K=1870.6\ \text{J}} \] \[ \boxed{\text{Answer = (A)}} \]
Step 1: Calculate the number of moles of \(CO_2\). Molar mass of \(CO_2\): \[ M=44\ \text{g mol}^{-1}. \] Given mass, \[ m=22\ \text{g}. \] Hence, \[ n=\frac{m}{M} =\frac{22}{44} =\frac12. \]
Step 2: Convert temperature into Kelvin. \[ T=27^\circ C+273. \] \[ T=300\ K. \]
Step 3: Calculate the translational kinetic energy. \[ K = \frac32 nRT. \] Substituting, \[ K = \frac32 \left(\frac12\right) (8.314)(300). \] \[ K = \frac34(2494.2). \] \[ K = 1870.65\ \text{J}. \] \[ K \approx 1870.6\ \text{J}. \] Therefore, \[ \boxed{K=1870.6\ \text{J}} \] \[ \boxed{\text{Answer = (A)}} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET kinetic theory Questions
- At what temperature is the root mean square (rms) speed of oxygen molecules ($O_2$) equal to that of helium molecules ($He$) at $27^\circ\text{C}$? (Given molar mass of $O_2 = 32\text{ g/mol}$, $He = 4\text{ g/mol}$)}
- The specific heat capacity of a gas at constant pressure ($C_p$) and at constant volume ($C_v$) are related as
- The mean free path of a gas molecule is inversely proportional to
- The mean free path of a gas molecule is inversely proportional to
- The rms speed of oxygen molecule at some temperature is $150 \text{ ms}^{-1}$. Then the rms speed of hydrogen molecule at the same temperature is
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions