Derive an expression for efficiency of a Carnot engine using T-S diagram. A Carnot engine has an efficiency of 50 percent when its sink temperature is at 27 ºC. Calculate the change in source temperature for increasing its efficiency to 60 percent.
In Isothermal process
P1V1=P2V2.......(1)
As B(V2,P2) and C(V3,P3) lies on same adibatic
P2V2γ=P3V3γ..........(2)
Again C and D lies on Sam isotherm
P3V3γ=P4V4γ.........+3)
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Derive the single-particle partition function for an ideal monatomic gas consisting of N identical particles occupying a volume V. Obtain expressions for the entropy and pressure of this system.
A system is subjected to 5 types of processes depicted in the table below. Using the first law of thermodynamics, fill up the blank spaces. All the entries are made in joules.
| Process | Heat added δQ | Work done δW | Internal Energy Initial (Ui) | Internal Energy Final (Uf) | Change in internal energy (dU) |
| I | 45 | 0 | - | 45 | - |
| II | - | 30 | 30 | - | 30 |
| III | 65 | - | 0 | - | 45 |
| IV | -20 | - | 15 | 40 | - |
| V | 85 | 50 | 40 | - | - |
Discuss the sedimentation in Brownian motion and show that during sedimentation, particle concentration decreases exponentially as height increases.
Two systems have thermodynamic probabilities of 3.0 1027 and 1.8
1028 respectively. Calculate the entropies of the individual systems and as well as their composite system and verify the Boltzmann relation.
Define viscosity. Discuss the effect of temperature and pressure on viscosity.
Consider a thermodynamic system consisting of 3 mol of an ideal gas occupying 0.03 m3 volume at 300 K temperature. Determine its initial pressure. For this gas, γ=1.4. It undergoes the following processes:
i) It is compressed to 0.01 m3 volume isothermally. Determine the pressure of the gas.
ii) then it is allowed to expand adiabatically, till it attains 1 atm pressure. Determine the final volume. (1 atm = 101325 Nm-2 )
Draw a labeled indicator diagram of these processes.
Explain with examples, what are reversible and irreversible processes? Why can a reversible process be attained only in a hypothetical situation?