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Important Questions on Thermometry, Thermal Expansion and Kinetic Theory of Gases

HARD
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 4
Show that the volume thermal expansion coefficient for an ideal gas at constant pressure is 1T.
HARD
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 5
The volume of a diatomic gas γ=75 is increased two times in a polytropic process with molar heat capacity, C=R. How many times will the rate of collision of molecules against the wall of the vessel be reduced as a result of this process?
HARD
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 1
A perfectly conducting vessel of volume, V=0.4 m3 contains an ideal gas at constant temperature, T=273 K. A portion of the gas is let out and the pressure of the gas falls by, Δp=0.24 atm. (Density of the gas at STP is ρ=1.2 kg m-3 ). Find the mass of the gas which escapes from the vessel.
HARD
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 2
A thin-walled cylinder of mass, m, height, h and cross-sectional area, A is filled with a gas and floats on the surface of water. As a result of leakage from the lower part of the cylinder, the depth of its submergence has increased by Δh. Find the initial pressure, p1 of the gas in the cylinder if the atmospheric pressure is, p0 and the temperature remains constant.
MEDIUM
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 3
Find the minimum attainable pressure of an ideal gas in the process ,T=T0+αV2, where, T0 and α are positive constants and V is the volume of one mole of gas.
MEDIUM
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 4
A solid body floats in a liquid at a temperature, t=50 °C being completely submerged in it. What percentage of the volume of the body is submerged in the liquid after it is cooled to t0=0 °C, if the coefficient of cubic expansion for the solid is γs=0.3×10-5 °C-1 and of the liquid γl=8×10-5  °C-1?
MEDIUM
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 5
Two vessels connected by a pipe with a sliding plug contain mercury. In one vessel, the height of mercury column is 39.2 cm and its temperature is 0 °C, while in the other, the height of mercury column is 40 cm and its temperature is 100 °C. Find the coefficient of cubical expansion for mercury. The volume of the connecting pipe should be neglected.
HARD
JEE Advanced
IMPORTANT
Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 4 - Thermometry, Thermal Expansion and Kinetic Theory of Gases>Exercises>Q 6

Two steel rods and an aluminum rod of equal length, l0 and equal cross-section are joined rigidly at their ends as shown in the figure below. All the rods are in a state of zero tension at 0 °C.

Steel
Aluminium
Steel

Find the length of the system when the temperature is raised to θ. Coefficient of linear expansion of aluminum and steel are αa and αs, respectively. Young's modulus of aluminum is Ya and of steel is Ys.