Write Onne’s equation. Using van der Waals’ equation, obtain an expression of
Boyle temperature (TB) in terms of van der Waals’ constants and hence show that the
Boyle’s temperature is related to critical temperature (TC) through the relation
TB = 3.375TC
Use van der Waals’ equation:
P is the pressure , Vm is molar volume, R is the universal gas constant, T is the absolute temperature, a,b constant van der Waals’ equation, find the function
P=P(V,T),, as a result we get and let T = const
Tc - temperature at which the difference between liquid and gas disappears,on the isotherms it corresponds to the inflection point (T=Tc), its
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A gaseous system expands from volume V1 to V2 under isobaric conditions.
Calculate the work done in this process.
Write Mayer’s formula. The molar heat capacities of a gas at constant pressure
and constant volume are 28.8 J mol−1 K−1 and 20.5 J mol−1 K−1 respectively.
Calculate the gas constant.
Consider a classical linear oscillator with
ε = p2/2m + bx2
where b is a constant. Assuming that the oscillator is in thermal equilibrium with a
heat reservoir at temperature T, calculate (i) the mean kinetic energy, (ii) the mean
potential energy for an assembly of N such oscillators.
the average height at which a molecule makes its last collision before crossing
the plane is
2λ.
3
Write the first law of thermodynamics for a gaseous system. Show that the
expression of difference of heat capacities of a gas at constant pressure and at
constant volume is given by
b) 2 kg of water is heated from 0°C to 100°C and converted into steam at the same temperature. Calculate the increase in entropy, given that specific heat of water is
4.18 × 103 J kg−1 K−1 and Latent heat of vaporisation is 2.27 × 107 J kg−1.
Using the Laplace formula, calculate the velocity of sound for air. Given γ = 1.4,
ρ = 1.29 kg m−3 and p = 1.01 × 105 Nm−2
The average energy of helium molecules is ¯E = 2.89 ×10−21J. Calculate their average speed (¯v).