I didnt realize how hard this class was and I am starting to get behind. If anyone can help me out a little (help with hw when I have it and other questions) I would gladly repay your time.
Stuck right now with:
1) Consider n moles of ideal gas kept in cylinder with a piston at external pressure p(0) with a heat contact to a reservoir with the temperature T. The external pressure is suddenly changed to p=2p(o), and we wait for the system to equilibrate.
a] Calculate the value V of the cylinder volume after equilibrium is reached.
b] Calculate the amount of work w, produced on the system, and applying the first law of thermodynamics calculate the amount q of heat, transferred from the system to the environment.
c] Calculate the amount of work w(rev) produced on the system and the amount of q(rev) of heat, transferred from the system to the environment, if the external pressure changes from p(0) to p=2p(0) very slowly, i.e., in a reversible process
d] Compare q with q(rev), i.e., find out whether q<q(rev), or it is the other way around. Provide a physical interpretation
And..
2) Consider n moles of ideal gas kept in a heat-isolated cylinder (all processes are adiabatic) with a piston at external pressure p(0), and at the temperature T(0). The external pressure is suddenly changed to p=2p(0), and we wait for the system to equilibrate. The volume and the temperature of the ideal gas after equilibration is V and T, respectively.
a] Calculate the amount of w of work produced on the system in terms of p, p(0), V, T(0), and n. Using the first law of thermodynamics, find a relation between V and T in terms of the inputs.
b] Using the relation between the external and internal pressure at equilibrium, combined with the equation of state for ideal gas, find another relation between V and T.
c] Considering the derived relations as a system of two equations on V and T, solve it, and find the values of V and T (i.e., after the equilibrium is reached.)
d] Using the relation between the pressure and the temperature for adiabatic processes in ideal gases, find the final temperature T(rev), if a slow (reversible) process is applied to increase the external pressure from p(0) to p=2p(0)
e] Compare T with T(rev), i.e., find out whether T<T(rev), or it is the other way around. Provide a physical interpretation
pm if you can help now, or in the future, thanks!