JEE Mains · Physics · STD 11 - Thermodynamics
- JEE Mains 2025
- Hard
- Numerical
The temperature of 1 mole of an ideal monoatomic gas is increased by \(50^{\circ} \mathrm{C}\) at constant pressure. The total heat added and change in internal energy are \(E_1\) and \(E_2\), respectively. If \(\frac{E_1}{E_2}=\frac{x}{9}\) then the value of \(x\) is _____
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) 15
Step-by-step Solution
Detailed explanation
Given that process is isobaric \(\Delta \mathrm{T}=50^{\circ} \mathrm{C}\)
Q in isobaric process \(=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}=\mathrm{E}_1\)
\(\Delta \mathrm{U}\) in isobaric process \(=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{E}_2\)
\(\therefore \frac{\mathrm{E}_1}{\mathrm{E}_2}=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{v}}}=\gamma\)
Given, gas is monoatomic
\(\begin{aligned}
\therefore \gamma & =1+\frac{2}{\mathrm{f}} \\
& =1+\frac{2}{3} \\
& =\frac{5}{3}
\end{aligned}\)
Now, as per question.
\(\begin{aligned}
& \frac{5}{3}=\frac{x}{9} \\
& x=15
\end{aligned}\)
Q in isobaric process \(=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}=\mathrm{E}_1\)
\(\Delta \mathrm{U}\) in isobaric process \(=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{E}_2\)
\(\therefore \frac{\mathrm{E}_1}{\mathrm{E}_2}=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{v}}}=\gamma\)
Given, gas is monoatomic
\(\begin{aligned}
\therefore \gamma & =1+\frac{2}{\mathrm{f}} \\
& =1+\frac{2}{3} \\
& =\frac{5}{3}
\end{aligned}\)
Now, as per question.
\(\begin{aligned}
& \frac{5}{3}=\frac{x}{9} \\
& x=15
\end{aligned}\)
More questions from Physics
- A small cube of side \(1\) mm is placed at the centre of a circular loop of radius \(10\) cm carrying a current of \(2\) A. The magnetic energy stored inside the cube is \(\alpha \times 10^{-14}\) J. The value of \(\alpha\) is _______. (\(\mu_o = 4\pi \times 10^{-7}\) Tm/A, \(\pi = 3.14\))JEE Mains 2026 Hard
- A body of mass \(m\) is taken from the surface of earth to a height equal to twice the radius of earth (\(R_e\)). The increase in potential energy will be _______.
(\(g\) is acceleration due to gravity at the surface of earth)JEE Mains 2026 Medium - A quantity Q is formulated as \(\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}\) and Z are independent parameters which have fractional errors of \(0.1,0.2\) and 0.5 , respectively in measurement. The maximum fractional error of Q is _______.JEE Mains 2025 Medium
- Find the truth table for the function \(Y\) and \(A\) and \(B\) represented in the following figure.
JEE Mains 2021 Medium - The mean free path of molecules of a certain gas at \(STP\) is \(1500\,d\), where \(d\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373\,K\) is approximately \(..........\,d\)JEE Mains 2023 Medium
- Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A diode under reverse-biased condition provides very small current which is nearly independent of voltage until a critical limit at which the current increases drastically.
Reason R: Below the critical voltage limit, only majority charge carriers flow which increases drastically above critical voltage.
Choose the correct answer from the options given belowJEE Mains 2026 Medium
More PYQs from JEE Mains
- A paramagnetic substance in the form of a cube with sides \(1\, cm\) has a magnetic dipole moment of \(20 \times 10^{-6}\, J/T\) when a magnetic intensity of \(60 \times 10^3\, A/m\) is applied. Its magnetic susceptibility isJEE Mains 2019 Medium
- A parallel plate capacitor has plate area \(100\, m ^{2}\) and plate separation of \(10\, m\). The space between the plates is filled up to a thickness \(5\, m\) with a material of dielectric constant of \(10 .\) The resultant capacitance of the system is \('x'\) \(pF\). The value of \(\varepsilon_{0}=8.85 \times 10^{-12} F \cdot m ^{-1}\) The value of \('x'\) to the nearest integer is............JEE Mains 2021 Hard
- An inductor of inductance \(10\) mH having resistance of \(100\,\Omega\) is connected to battery of E.M.F. \(1.0\) V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is \(2\) mA and \(4\) mA is _______.
JEE Mains 2026 Hard - A sample of gas with \(\gamma=1.5\) is taken through an adiabatic process in which the volume is compressed from \(1200\, {cm}^{3}\) to \(300\, {cm}^{3}\). If the initial pressure is \(200\, {kPa}\). The absolute value of the workdone by the gas in the process \(= \,..... J.\)JEE Mains 2021 Hard