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Obtain the Boltzmann relation between
entropy and thermodynamic probability.
Discuss its significance.

 The mean free path of the molecules of 

a gas at 27°C is 6.0 x 10-8 m. Calculate 

the pressure exerted by the gas. 

The radius of the molecule is 1.8 A. 

Take kB= 1.38x 10-23J K -1.


State the third law of thermodynamics and show that the heat capacities of a substance converge as T - 0 .
Define the term adiabatic lapse rate. obtain an expression for adiabatic lapse rate for the earth atmosphere.
A gas undergoes adiabatic transformation using the first law of thermodynamics show that this process is represented by the equation pVy =constant
A unit mass of a fluid was compressed reversibly from 2 bar, 0.39 m3
to 14 bar
and 0.09 m3 according to a linear law. The fluid is then cooled reversibly at
constant pressure, and finally expanded isothermally to the initial conditions.
Calculate the work done on/by the fluid in each process, the net work and
sketch the processes on a Pressure-Volume diagram?
Consider a gas sample of 12 g of oxygen (O_2) in a container, and it is heated at constant pressure, and when heated its temperature increases from 25⁰C to 125⁰C. (a) Calculate number of moles of oxygen present, (b) How much energy is transferred to oxygen gas as heat, keeping in mind that molecules rotate but do not vibrate. (c) What fraction of the heat is used to increase the internal energy of the oxygen?
Consider a gas sample of 12 g of oxygen (O_2) in a container, and it is heated at constant pressure, and when heated its temperature increases from 25⁰C to 125⁰C. (a) Calculate number of moles of oxygen present, (b) How much energy is transferred to oxygen gas as heat, keeping in mind that molecules rotate but do not vibrate. (c) What fraction of the heat is used to increase the internal energy of the oxygen?
Suppose molar specific heat C_V of iron is given by C_V=AT^5, where A is some constant. For iron, A=5.17×〖10〗^(-3) J⁄(mol .K^4 ). Calculate the entropy change for 2.00 mol of iron when its temperature increases from 15 K to 25 K.

At the beginning of compression a cylinder contains 800 cm3 of gas at a pressure of 130kN/m2 absolute. Compression takes place according to the law PVn = constant until the pressure is 750kN/m2. If the final volume is 1/5 of the initial volume, determine the value of polytropic process index n.


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