Question:
An ideal monoatomic gas of \(1.5\) moles is heated at a constant pressure of \(2\,\text{atm}\) so that its temperature increases from \(30^\circ\text{C}\) to \(130^\circ\text{C}\). Work done by the gas is \((R=8.3\,\text{J mol}^{-1}\text{K}^{-1})\)
An ideal monoatomic gas of \(1.5\) moles is heated at a constant pressure of \(2\,\text{atm}\) so that its temperature increases from \(30^\circ\text{C}\) to \(130^\circ\text{C}\). Work done by the gas is \((R=8.3\,\text{J mol}^{-1}\text{K}^{-1})\)
Show Hint
For an ideal gas undergoing an isobaric process,
\[
W=P\Delta V=nR\Delta T.
\]
You do not need the pressure value explicitly once \(n\), \(R\), and \(\Delta T\) are known.
Updated On: Jun 18, 2026
- \(2500\,\text{J}\)
- \(1450\,\text{J}\)
- \(1245\,\text{J}\)
- \(555\,\text{J}\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Use the work done formula for a constant pressure process.
For an isobaric process, \[ W=P\Delta V \] Using the ideal gas equation, \[ PV=nRT \] At constant pressure, \[ P\Delta V=nR\Delta T \] Therefore, \[ W=nR\Delta T \]
Step 2: Calculate the change in temperature.
Initial temperature, \[ T_1=30^\circ\text{C} \] Final temperature, \[ T_2=130^\circ\text{C} \] Hence, \[ \Delta T=T_2-T_1 \] \[ \Delta T=130-30 \] \[ \Delta T=100\,\text{K} \]
Step 3: Substitute the given values.
Given, \[ n=1.5 \] \[ R=8.3\,\text{J mol}^{-1}\text{K}^{-1} \] \[ \Delta T=100\,\text{K} \] Therefore, \[ W=nR\Delta T \] \[ W=1.5\times 8.3\times 100 \] \[ W=1245\,\text{J} \]
Step 4: Final conclusion.
Hence, the work done by the gas is \[ \boxed{1245\,\text{J}} \]
For an isobaric process, \[ W=P\Delta V \] Using the ideal gas equation, \[ PV=nRT \] At constant pressure, \[ P\Delta V=nR\Delta T \] Therefore, \[ W=nR\Delta T \]
Step 2: Calculate the change in temperature.
Initial temperature, \[ T_1=30^\circ\text{C} \] Final temperature, \[ T_2=130^\circ\text{C} \] Hence, \[ \Delta T=T_2-T_1 \] \[ \Delta T=130-30 \] \[ \Delta T=100\,\text{K} \]
Step 3: Substitute the given values.
Given, \[ n=1.5 \] \[ R=8.3\,\text{J mol}^{-1}\text{K}^{-1} \] \[ \Delta T=100\,\text{K} \] Therefore, \[ W=nR\Delta T \] \[ W=1.5\times 8.3\times 100 \] \[ W=1245\,\text{J} \]
Step 4: Final conclusion.
Hence, the work done by the gas is \[ \boxed{1245\,\text{J}} \]
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