Use R=8.3 J/mol-K wherever required.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. $2 \mathrm{~g}$ of hydrogen is sealed in vessel of volume $0.02 \mathrm{~m}^{3}$ and is aintained at $300 \mathrm{~K}$. Calculate the pressure in the vessel. 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. A gas cylinder has walls that can bear a maximum pressure of $1.0^{\times 10^{6}}$ Pa. It contains a gas at $8.0$ $\times 10^{5} \mathrm{~Pa}$ and $300 \mathrm{~K}$. The cylinder is steadily heated. Neglecting any change in the volume, calculate the temperature at which the cylinder will break. Solution:...
Read More →Use R=8.3 J/mol-K wherever required.
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. An electric bulb of volume 250 cc was sealed during manufacturing at a pressure of $10^{-3} \mathrm{~mm}$ of mercury at $27^{\circ} \mathrm{C}$. Compute the number of air molecules contained in the bulb. Avogadro constant $=6^{\times} 10^{23}$ per $\mathrm{mol}$, density of mercury $=13600 \mathrm{~kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$. 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. Equal of masses of air are sealed in two vessels, one of volume $V_{0}$ and the other of volume $2 V_{0}$. If the first vessel is maintained at a temperature $300 \mathrm{~K}$ and the other at $600 \mathrm{~K}$, find the ratio of the pressures in the two vessels. 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. Calculate the mass of $1 \mathrm{~cm}^{3}$ of oxygen kept at STP. 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. Find the number of molecules in $1 \mathrm{~cm}^{3}$ of an ideal gas at $0^{\circ} \mathrm{C}$ and at a pressure of $10^{-5} \mathrm{~mm}$ of mercury. 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. Find the number of molecules of an ideal gas in a volume of $1.00 \mathrm{~cm}^{3}$ at STP. 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. Calculate the volume of 1 mole of an ideal gas at STP. Solution:...
Read More →A circular disc made of iron is rotated about its axis
Question: A circular disc made of iron is rotated about its axis at a constant velocity $\omega$. Calculate the percentage change in the linear speed of the particle of the rim as the disc is slowly heated from $20^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ keeping the angular velocity constant. Coefficient of linear expansion of iron= $1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}$. Solution:...
Read More →A torsional pendulum consists of a solid disc connected
Question: A torsional pendulum consists of a solid disc connected to a thin wire $\left(\alpha=2.4 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$ at its center. Find the percentage change in the time period between peak winter $\left(5^{\circ} \mathrm{C}\right)$ and peak summer $\left(45^{\circ} \mathrm{C}\right)$. Solution:...
Read More →Show that moment of inertia of a solid body
Question: Show that moment of inertia of a solid body of any shape changes with temperature as $I=I_{0}(1+2 \alpha \theta)$ where $I_{0}$ is the moment of inertia at $0^{\circ} \mathrm{C}$ and $\alpha$ is the coefficient of linear expansion of the solid. Solution:...
Read More →A steel ball initially at a pressure of
Question: A steel ball initially at a pressure of $1.0^{\times 10^{5}} \mathrm{~Pa}$ is heated from $20^{\circ} \mathrm{C}$ to $120^{\circ} \mathrm{C}$ keeping its volume constant. Find the inside the ball. Coefficient of linear expansion of steel $=12^{\times 10^{-6} /{ }^{\circ} \mathrm{C}}$ and bulk modulus of steel $=1.6^{\times 10^{11} \mathrm{~N} / \mathrm{m}^{2}}$. Solution:...
Read More →Two steel rods and an aluminium rod of equal length
Question: Two steel rods and an aluminium rod of equal length $l_{0}$ and equal cross-section are joined rigidly at their ends as shown in figure below. All the rods are in the state of zero tension at $0^{\circ} \mathrm{C}$. Find the length of the system when the temperature is raised to $\theta$. Coefficient of linear expansion of aluminium and steel are $\alpha_{a}$ and $\alpha_{s}$ respectively. Young's modulus of aluminium is $Y_{a}$ and of steel is $Y_{s}$. Solution:...
Read More →A steel rod is rigidly clamped at two ends.
Question: A steel rod is rigidly clamped at two ends. The rod is under zero tension at $20^{\circ} \mathrm{C}$. If the temperature rises to $100^{\circ} \mathrm{C}$, what force will the rod exert on one of the clamps. Area of cross-section of the rod=2.00 $\mathrm{mm}^{2}$. Solution:...
Read More →A steel wire of cross-sectional area
Question: A steel wire of cross-sectional area $0.5 \mathrm{~mm}^{2}$ is held between two fixed supports. If the wire is just taut at $20^{\circ} \mathrm{C}$, determine the tension when the temperature falls to $0^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel is $1.2^{\times 10^{-5} /{ }^{\circ} \mathrm{C}}$ and its Young'smodulus is $2.0^{\times 10^{11}} \mathrm{~N} / \mathrm{m}^{2}$ Solution:...
Read More →A steel rod is clamped at its two ends and rests on fixed horizontal base.
Question: A steel rod is clamped at its two ends and rests on fixed horizontal base. The rod is unstrained at $20^{\circ} \mathrm{C}$ Find the longitudinal strain developed in the rod if the temperature rises to $50^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel $=1.2^{\times 10^{-5} /{ }^{\circ} \mathrm{C}}$ Solution:...
Read More →A steel rod of length 1 m rests on a smooth horizontal base.
Question: A steel rod of length $1 \mathrm{~m}$ rests on a smooth horizontal base. If it is heated from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$, what is the longitudinal strain developed? Solution: Since, there is no opposition in expansion of length, no stress develops and hence no longitudinal strain developed....
Read More →The densities of wood and benzene at
Question: The densities of wood and benzene at $0^{\circ} \mathrm{C}$ are $880 \mathrm{~kg} / \mathrm{m}^{3}$ and $900 \mathrm{~kg} / \mathrm{m}^{3}$ respectively. The coefficients of volume expansion are $1.2^{\times 10^{-3} /{ }^{\circ} \mathrm{C}}$ for wood and $1.5^{\times 10^{-3}} /{ }^{\circ} \mathrm{C}$ for benzene. At what temperature will a piece of wood just sink in benzene? Solution:...
Read More →The densities of wood and benzene at
Question: The densities of wood and benzene at $0^{\circ} \mathrm{C}$ are $880 \mathrm{~kg} / \mathrm{m}^{3}$ and $900 \mathrm{~kg} / \mathrm{m}^{3}$ respectively. The coefficients of volume expansion are $1.2^{\times 10^{-3} /{ }^{\circ} \mathrm{C}}$ for wood and $1.5^{\times 10^{-3}} /{ }^{\circ} \mathrm{C}$ for benzene. At what temperature will a piece of wood just sink in benzene? Solution:...
Read More →A glass vessel measures exactly 10 cm×10 cm ×10 cm
Question: A glass vessel measures exactly $10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm}$ at $0^{\circ} \mathrm{C}$. It is completely filled with the mercury at this temperature. When the temperature is raised to $10^{\circ} \mathrm{C}, 1.6 \mathrm{~cm}^{3}$ of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass $=6.5^{\times 10^{-6} /{ }^{\circ} \mathrm{C}}$. Solution:...
Read More →An aluminium can of cylindrical shape contains
Question: An aluminium can of cylindrical shape contains $500 \mathrm{~cm}^{3}$ of water. The area of inner cross-section of the can is $125^{\mathrm{cm}^{2}}$. All measurements refer to $10^{\circ} \mathrm{C}$. Find the rise in the water level if the temperature increases to $80^{\circ} \mathrm{C}$. The coefficient of linear expansion of aluminium $=23^{\times 10^{-6} /{ }^{\circ} \mathrm{C}}$ and the average coefficient of volume expansion of water $=3.2^{\times 10^{-4}} /{ }^{\circ} \mathrm{C...
Read More →The volume of a glass vessel is 1000 cc at
Question: The volume of a glass vessel is 1000 cc at $20^{\circ} \mathrm{C}$. What volume $v$ of mercury should be poured into it at this temperature so that the volume of the remining space does not change with temperature? Coefficients of cubical expansion of mercury and glass are $1.8^{\times 10^{-4} /{ }^{\circ} \mathrm{C}}$ and $9.0^{\times 10^{-6} /{ }^{\circ} \mathrm{C}}$ respectively. Solution:...
Read More →A glass window is to be fit in an aluminium frame.
Question: A glass window is to be fit in an aluminium frame. The temperature on the working day is $40{ }^{\circ} \mathrm{C}$ and the glass window measures exactly $20 \mathrm{~cm} \times 30 \mathrm{~cm}$. What should be the size of the aluminium frame so that there is no stress on the glass in winter even if the temperature drops to $0^{\circ} \mathrm{C}$ ? Coefficients of linear Solution:...
Read More →An aluminium plate fixed in a horizontal position has a hole diameter
Question: An aluminium plate fixed in a horizontal position has a hole diameter $2.000 \mathrm{~cm}$. A steel sphere of diameter $2.005 \mathrm{~cm}$ rests on this hole. All the lengths refer to a temperature of $10^{\circ} \mathrm{C} .$ The temperature of the entire system is slowly increased. At what temperature will the fall down? Coefficient of linear expansion of aluminium is $23^{\times 10^{-6}} /{ }^{\circ} \mathrm{C}$ and that of steel is $11^{\times 10^{-6}} /{ }^{\circ} \mathrm{C}$. So...
Read More →A pendulum clock gives correct time at
Question: A pendulum clock gives correct time at $20^{\circ} \mathrm{C}$ at a place where, $g=9.800 \mathrm{~m} / s^{2}$. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where $\mathrm{g}=9.788 \mathrm{~m} / \mathrm{s}^{2}$. At what temperature will it give correct time? Coefficient of linear expansion of steel $=12^{\times 10^{-6} /{ }^{\circ} \mathrm{C}}$. Solution:...
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