Molecular Physics | Thermodynamics Answers

A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 above ground on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 × 103kg/m3. Find the difference in pressure between the main line and the second floor.

In one line simple sentence for each, state four implications of Newton's first law of motion

when the temperature of a radiated block body increases the maximum intensity of radiation
1) shift towards the largest wavelength
2)shift towards the shorter wavelength
3)remains unaffected
4)depends on the ambient temperature

Name the processes that comprise a Carnot cycle. Prove that its efficiency is maximum and always less than one.

Starting with the equation of motion, prove that the phase space of a linear harmonic oscillator is elliptical.

Two identical gas systems, each containing 0.1 mole of ideal gas, are at 300 K and 3 atm pressure. One system is allowed to expand adiabatically and the other isothermally, till both attain normal pressure. Show that the volume of adiabatically expanded
system is less than the isothermally expanded system. The ratio of the heat capacities of the gas is
1.4.

Using the expression for the partition function of an N-particle ideal gas, obtain the expression for its entropy

Derive the expression for the work done by one mole of van der Waals gas during the isothermal expansion from volume V1, to V2 at temperature T.

Starting from the expression for thermodynamic probability for a Fermi system, obtain expression for its distribution function.

What are the macroscopic properties of a system? Explain the difference between the lntensive and extensive variables. Mention the intensive and extensive variables for a gas in a cylinder.