Question:
A vessel has \(6\) gram of hydrogen at pressure \(P\) and temperature \(500\) K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is \(\frac{P}{2}\) and the temperature falls to \(300\) K?
A vessel has \(6\) gram of hydrogen at pressure \(P\) and temperature \(500\) K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is \(\frac{P}{2}\) and the temperature falls to \(300\) K?
Show Hint
The vessel volume is fixed, so $n\propto P/T$.
Updated On: Oct 1, 2026
- \(2\) gram
- \(3\) gram
- \(4\) gram
- \(1\) gram
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Use the gas equation
\(PV=nRT\) with fixed \(V\) gives \(n\propto\frac{P}{T}\).
Step 2: Ratio
\(\frac{n_2}{n_1}=\frac{P/2}{300}\times\frac{500}{P}=\frac{5}{6}\).
Step 3: Mass left and lost
Mass left \(=\frac56\times6=5\) g, so \(6-5=1\) g leaks out. Option (D).
Final Answer:
One gram of hydrogen leaks out, option (D). \[ \boxed{\text{(D) }1\text{ g}} \]
\(PV=nRT\) with fixed \(V\) gives \(n\propto\frac{P}{T}\).
Step 2: Ratio
\(\frac{n_2}{n_1}=\frac{P/2}{300}\times\frac{500}{P}=\frac{5}{6}\).
Step 3: Mass left and lost
Mass left \(=\frac56\times6=5\) g, so \(6-5=1\) g leaks out. Option (D).
Final Answer:
One gram of hydrogen leaks out, option (D). \[ \boxed{\text{(D) }1\text{ g}} \]
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 Ideal gas equation Questions
- To double the pressure of an ideal gas, keeping volume and number of moles constant, the temperature should be:
- An ideal gas at pressure ' P ' and temperature ' T ' is enclosed in a vessel of volume ' $V$ '. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to ' $\text{P}'$ '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is
- An ideal gas at pressure ' P ' and temperature ' T ' is enclosed in a vessel of volume ' $V$ '. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to ' $\text{P}'$ '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is
- A balloon is filled at 27$^\circ$C and 1 atmospheric pressure by volume 500 m$^3$ helium gas. At -3$^\circ$C and 0.5 atmospheric pressure, the volume of helium gas will be ______.
- Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters \(2P\), \(\frac{V}{4}\), \(2T\). The ratio of number of molecules of jar B to those of jar A is
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