Question:
Two cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at 303 K. The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 63 K then the rise in temperature of the gas in A is
Two cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at 303 K. The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 63 K then the rise in temperature of the gas in A is
Show Hint
Average translational energy of a molecule is 3/2 kT; an electron accelerated through V gets eV.
Updated On: Oct 1, 2026
- \(35\) K
- \(40\) K
- \(45\) K
- \(50\) K
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Average translational kinetic energy of a gas molecule is \(E_1 = \frac32kT\), where \(k = \frac{R}{N}\). The electron gains \(E_2 = eV\).
Step 2: Equate:
\[ \frac32\cdot\frac{R}{N}T = eV \Rightarrow T = \frac{2eVN}{3R} \]
Here N is the Avogadro-type number of molecules per mole and R is the gas constant, so \(\frac RN\) is the Boltzmann constant.
Final Answer:
The temperature is \(\frac{2eVN}{3R}\), option (B). \[ \boxed{T = \frac{2eVN}{3R}} \]
Average translational kinetic energy of a gas molecule is \(E_1 = \frac32kT\), where \(k = \frac{R}{N}\). The electron gains \(E_2 = eV\).
Step 2: Equate:
\[ \frac32\cdot\frac{R}{N}T = eV \Rightarrow T = \frac{2eVN}{3R} \]
Here N is the Avogadro-type number of molecules per mole and R is the gas constant, so \(\frac RN\) is the Boltzmann constant.
Final Answer:
The temperature is \(\frac{2eVN}{3R}\), option (B). \[ \boxed{T = \frac{2eVN}{3R}} \]
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Kinetic molecular theory of gases Questions
- Two perfect gases at absolute temperatures $T_1$ and $ T_2$ are mixed. There is no loss of energy. The temperature of mixture of masses of molecules are $ m_1$ and $ m_2$ and the number of molecules in the gases are $n_1 $ and $ n_2 $ respectively, is
- If $m$ represents the mass of each molecule of a gas and $T$ its absolute temperature, then the root mean square speed of the gas molecule is proportional to
- An insulated container contains a monoatomic gas of molar mass 'm'. The container is moving with velocity 'V'. If it is stopped suddenly, the change in temperature of the gas is (R-gas constant)
- Energy of a gas/litre is \(600\) joule, then what will be its pressure?
- A rigid diatomic gas having molar mass m is contained in an insulated container. The container is moving with velocity V. If it is stopped suddenly, the change in temperature is (R - gas constant)
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions