MHT CET · Physics · Thermodynamics
In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged \((\mathrm{Q})\) is \(\left(\gamma=\frac{C_p}{C_v}\right)\)
- A \(\gamma\)
- B \(\gamma-1\)
- C \(\frac{\gamma}{\gamma-1}\)
- D \(\frac{\gamma-1}{\gamma}\)
Answer & Solution
Correct Answer
(D) \(\frac{\gamma-1}{\gamma}\)
Step-by-step Solution
Detailed explanation
In isobaric process,
Heat exchanged, \(Q=n_P \Delta T\)
and work done, \(\mathrm{W}=\mathrm{n}\left(\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}\right) \Delta \mathrm{T}\)
\(\begin{array}{ll}
\therefore \quad & \frac{W}{Q}=1-\frac{C_v}{C_p} \\
& \text { but } \gamma=\frac{C_p}{C_v} \\
\therefore \quad & \frac{W}{Q}=1-\frac{1}{\gamma}=\frac{\gamma-1}{\gamma}
\end{array}\)
Heat exchanged, \(Q=n_P \Delta T\)
and work done, \(\mathrm{W}=\mathrm{n}\left(\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}\right) \Delta \mathrm{T}\)
\(\begin{array}{ll}
\therefore \quad & \frac{W}{Q}=1-\frac{C_v}{C_p} \\
& \text { but } \gamma=\frac{C_p}{C_v} \\
\therefore \quad & \frac{W}{Q}=1-\frac{1}{\gamma}=\frac{\gamma-1}{\gamma}
\end{array}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- If ' \(\mathrm{n}_{\mathrm{e}}\) ' and ' \(\mathrm{n}_{\mathrm{h}}\) ' are the number of electrons and number of holes respectively in a semiconductor heavily doped with phosphorous thenMHT CET 2024 Easy
- When a capacitor is connected in series LR circuit, the alternating current flowing in the circuitMHT CET 2025 Easy
- In biprism experiment, if \(5^{\text {th }}\) bright band with wavelength \({ }^{\prime} \lambda_{1}{ }^{\prime}\) coincides with \(6^{\text {th }}\) dark band with wavelength \(^{\prime} \lambda_{2}\) ' then the ratio \(\left(\frac{\lambda_{2}}{\lambda_{1}}\right)\) isMHT CET 2020 Medium
- Three charges each of value \(+q\) are placed at the corners of an isosceles triangle \(\mathrm{ABC}\) of sides \(\mathrm{AB}\) and \(\mathrm{AC}\) each equal to \(2 \mathrm{a}\). The mid points of \(A B\) and \(A C\) are \(D\) and \(E\) respectively. The work done in taking a charge \(\mathrm{Q}\) from \(\mathrm{D}\) to \(\mathrm{E}\) is \(\left(\varepsilon_0=\right.\) permittivity of free space)MHT CET 2023 Hard
- In an NPN transistor \(10^{10}\) electrons enter the emitter in \(10^{-6} \mathrm{~s}\) and \(2 \%\) electrons recombine with holes in base. The current ratios ' \(\alpha\) ' and ' \(\beta\) ' of a transistor are respectively (nearly)MHT CET 2024 Hard
- If a capillary tube of radius \(1 \mathrm{~mm}\) is immersed in water, the mass of water rising in the capillary tube is \(\mathrm{m}\). If the radius of the capillary tube is doubled, then the mass of water that rises in the same capillary tube will beMHT CET 2022 Medium
More PYQs from MHT CET
- Identify thermoplastic polymer from followingMHT CET 2020 Easy
- The unit of Wien's constant \(b\) isMHT CET 2009 Easy
- If \(|\overline{\mathrm{a}}|=3 ;|\overline{\mathrm{b}}|=5 ; \overline{\mathrm{b}} \cdot \overline{\mathrm{c}}=10\), angle between \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) is \(\frac{\pi}{3}, \overline{\mathrm{a}}\) is perpendicular to \(\overline{\mathrm{b}} \times \overline{\mathrm{c}}\). Then the value of \(|\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})|\) isMHT CET 2023 Medium
- If the slopes of the lines given by the equation \(a x^2+2 h x y+b y^2=0\) are in the ratio \(5: 3\), then ration \(h^2: a b=\)MHT CET 2021 Medium
- The population of a village increases at a rate proportional to the population at that time. In a period of 10 years the population grew from 20,000 to 40,000 , then the population after another 20 years isMHT CET 2020 Medium
- A stone is projected at angle ' \(\theta\) ' with velocity ' \(u\) '. If it executes nearly a circular motion at its maximum point for short time, the radius of the circular path will be ( \(\mathrm{g}=\) acceleration due to gravity)MHT CET 2022 Easy