Use R=8.3 J/mol-K wherever required. A uniform tube closed at one end,
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A uniform tube closed at one end, contains a pallet of mercury $10 \mathrm{~cm}$ long. When the tube is kept vertically with the closed end upward, the length of the air column trapped is $20 \mathrm{~cm}$. Find the length of the air column trapped when the tube is inverted so that the closed end goes down. Atmospheric pressure $=75 \mathrm{~cm}$ of mercury. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. A container of volume 50°C contains air (mean molecular weight=28.8 g)
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A container of volume $50^{\circ} \mathrm{C}$ contains air (mean molecular weight= $28.8 \mathrm{~g}$ ) and is open to atmosphere when the pressure is $100 \mathrm{kPa}$. The container is kept in a bath containing melting ice ( $\left.0^{\circ} \mathrm{C}\right)$. (a) Find the mass of the air in the container when thermal equilibrium is reached. (b) The container is now placed in another bath containing boili...
Read More →Use R=8.3 J/mol-K wherever required. Figure shows two vessels A and B with
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Figure shows two vessels $\mathrm{A}$ and $\mathrm{B}$ with rigid walls containing ideal gases. The pressure, temperature and the volume are $\rho_{A}, T_{A}, V$ in the vessel $\mathrm{A}$ and $\rho_{B}, T_{B}, V$ in the vessel B. The vessels are now connected through a small tube. Show that the pressure $p$ and the temperature $T$ satisfy $\frac{p}{T}=\frac{1}{2}\left(\frac{p_{A}}{T_{A}}+\frac{\rho_{B}}{T_{B...
Read More →Use R=8.3 J/mol-K wherever required. A vertical cylinder of height 100 cm contains
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A vertical cylinder of height $100 \mathrm{~cm}$ contains air at a constant temperature. The top is closed by a frictionless light piston. The atmospheric pressure is equal to $75 \mathrm{~cm}$ of mercury. Mercury is slowly poured over the piston. Find the maximum height of the mercury column that can be put on the piston. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. A vessel contains 1.60 g of oxygen and
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A vessel contains $1.60 \mathrm{~g}$ of oxygen and $2.80 \mathrm{~g}$ of nitrogen. The temperature is maintained at $300 \mathrm{~K}$ and volume of the vessel is $0.166 \mathrm{~m}^{3}$. Find the pressure of the mixture. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. During an experiment, an ideal gas is found
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. During an experiment, an ideal gas is found to obey an additional law $p V^{2}=$ constant. The gas is initially at a temperature T and a volume V. Find the temperature when it expands to a volume $2 \mathrm{~V}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. 0.040 g of He is kept in a closed container
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. $0.040 \mathrm{~g}$ of He is kept in a closed container initially at $100.0^{\circ} \mathrm{C}$. The container is now heated. Neglecting the expansion of the container, calculate the temperature at which the internal energy is increased by $12 \mathrm{~J}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is $0.002^{m^{3}}$. One of the tubes gets punctured and the volume of the tube reduces to $0.0005^{m^{3}}$. How many moles of air have leaked out? Assume that the temperature remains constant at $300 \mathrm{~K}$ and that the air behaves as an ideal gas. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. An air bubble of radius 2.0 mm is formed
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. An air bubble of radius $2.0 \mathrm{~mm}$ is formed at the bottom of a $3.3 \mathrm{~m}$ deep river. Calculate the radius of the bubble as it comes to the surface. Atmospheric pressure $=1.0 \times 10^{5} \mathrm{~Pa}$ and density of water=1000 kg/ $\mathrm{m}^{3}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Oxygen is filled in a closed jar of
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Oxygen is filled in a closed jar of volume $1.0 \times 10^{-3} \mathrm{~m}^{3}$ at a pressure of $1.5 \times 10^{5} \mathrm{~Pa}$ and temperature $400 \mathrm{~K}$. The jar has a small leak in it. The atmospheric pressure is $1.0 \times 10^{5} \mathrm{~Pa}$ and the atmospheric temperature is $300 \mathrm{~K}$. Find the mass of the gas that leaks out by the time the pressure and the temperature inside the jar ...
Read More →Use R=8.3 J/mol-K wherever required. Air is pumped into an automobile tyre's tube
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Air is pumped into an automobile tyre's tube upto a pressure of $200 \mathrm{kPa}$ in the morning when the air temperature is $20^{\circ} \mathrm{C}$. During the day the temperature rises to $40^{\circ} \mathrm{C}$ and the tube expands by $2 \%$. Calculate the pressure of the air in the tube at this temperature. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Hydrogen gas is contained in a closed vessel
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Hydrogen gas is contained in a closed vessel at $1 \mathrm{~atm}(100 \mathrm{kPa})$ and $300 \mathrm{~K}$. (a) Calculate the mean speed of the molecules. (b) Suppose the molecules strike the wall with this speed making an average angle of $45^{\circ}$ with it. How many molecules strike each square meter of the wall per second? Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Estimate the number of collisions per second suffered
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) $=1.38 \times 10^{-5}$ $\mathrm{cm}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Figure shows a vessel partitioned by a fixed diathermic separator.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Figure shows a vessel partitioned by a fixed diathermic separator. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left part equals the mean speed of the molecules in the right. Calculate the ratio of the mass of a molecule molecule in the left part of the mass of a molecule in the right part. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Find the ratio of the mean speed of hydrogen molecules
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Find the ratio of the mean speed of hydrogen molecules to the mean speed of nitrogen molecules in a sample containing a mixture of two gases. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. At what temperature the mean speed of the molecules
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth? Solution:...
Read More →Use R=8.3 J/mol-K wherever required. The mean speed of the molecules of a hydrogen sample
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The mean speed of the molecules of a hydrogen sample equals to the speed of the molecules of helium sample. Calculate the temperature of the hydrogen sample to the temperature of the helium sample. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Find the average magnitude of linear momentum of
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Find the average magnitude of linear momentum of a helium molecule in a sample of helium gas at $0^{\circ} \mathrm{C}$. Mass of a helium molecule $=6.64 \times 10^{-27} \mathrm{~kg}$ and Boltzmann constant $=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Consider a sample of oxygen at 300 K.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Consider a sample of oxygen at $300 \mathrm{~K}$. Find the average time taken by a molecule to travel a distance equal to the diameter of the earth. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. The average translational kinetic energy of
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The average translational kinetic energy of air molecules is $0.040 \mathrm{eV}\left(1 \mathrm{eV}=1.1 \times 10^{-19} \mathrm{~J}\right)$. Calculate the temperature of the air. Boltzmann constant $\mathrm{k}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. A sample of 0.177 g of an ideal gas
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A sample of $0.177 \mathrm{~g}$ of an ideal gas occupies $1000 \mathrm{~cm}^{3}$ at STP. Calculate the rms speed of the gas molecules. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Find the rms speed of hydrogen molecules
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Find the rms speed of hydrogen molecules in a sample of hydrogen gas at $300 \mathrm{~K}$. Find the temperature at which the rms speed is double the speed calculated in the previous part. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Figure shows a cylindrical tube
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Figure shows a cylindrical tube with adiabatic walls and fitted with a diathermic separator. The separator can be slid in the tube by an external mechanism. An ideal gas is injected in the two sides at equal pressures and equal temperatures. The separator remains in equilibrium at the middle. It is now solid to a position where it divides the tube in the ratio of $1: 3$. Find the ratio of the pressures in the...
Read More →Use R=8.3 J/mol-K wherever required.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The temperature and pressure at Shimla are $15.0^{\circ} \mathrm{C}$ and $72.0 \mathrm{~cm}$ of mercury and at Kalka these are $35.0^{\circ} \mathrm{C}$ and $76.0 \mathrm{~cm}$ of mercury. Find the ratio of air density at Kalka to the air density at Shimla. Solution:...
Read More →Use R=8.3 J/mol-K wherever required.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The density of an ideal gas is $1.25 \times 10^{-3} \mathrm{~g} / \mathrm{cm}^{3}$ at STP. Calculate the molecular weight of the gas. Solution:...
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