State second law of thermodynamics in as many forms as

Question

1. Evaluate the value of constant A and β from following relation

dn_c = 4πN(m/2πkT)^3/2C²e^-mC2/2kTdC

2. During change in state for 3 moles of an ideal gas the temperature change by 2K at both constant V and p. Calculate ?U and ?H (given Cp=5/2R).

3. State third law of thermodynamic. what is its limitation also derives its mathematical form.

4. State second law of thermodynamics in as many forms as possible and show that they are identical in significance.