a) A block of metal whose volume expansivity is and isothermal compressibility is
has volume 5 litre at 1 atm and
. On applying pressure, its temperature rises by
applying pressure, its temperature rises by and volume increases by 0.5
Calculate the pressure applied.
We will use the thermodynamic relation between volume expansivity (β), isothermal compressibility (κ), and the changes in temperature (ΔT), pressure (ΔP), and volume (ΔV): \[ \frac{\Delta V}{V} = \beta \Delta T - \kappa \Delta P \] ### Given Data: - Volume expansivity: \( \beta = 5.0 \times 10^{-5} \, __________ ___ ___ __________ ___ _______ _____.
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c) Using the expression of Bose-Einstein distribution function for photons
derive Plancks Law and show that (i) Rayleigh-Jeans Law, and (ii) Wien’s Law follow from it at low & high frequencies.
The mean speed of oxygen molecules is 450
If the radius of an oxygen molecule is 1.8 Å, calculate mean time between two successive collisions and mean free path. Take
b) Define adiabatic lapse rate? Obtain an expression for adiabatic lapse rate for earth’s atmosphere?
b) Draw Carnot cycle on (i) and (ii)
diagrams. With the help of diagram, show tha
where
is the amount of heat absorbed at temperature
and
is the amount of heat rejected at temperature
b) What is a Gibbs paradox? How did it arise?
a) State the principle of equipartition of energy. Write a relation between number of degrees of freedom, number of particles constituting the system and the total number of constraints. Calculate the degrees of freedom for (i) single atom, (ii) diatomic molecule.
b) Explain the working of a platinum resistance thermometer with the help of a neat and labelled diagram. State the reasons for using platinum for the construction of a resistance thermometer.