consider n moles of ideal gas kept in a heat isolated cylinder (all processes ar

Question

consider n moles of ideal gas kept in a heat isolated cylinder (all processes are adiabatic) with a piston at extrnal pressure P(i), and at the temperature T(i). the extrnal pressure is suddenly changed to P=2P(i), and we wait for the system to equilibrate. the volume and the temprature of the ideal gas after equilibration is V and T, respectivly.(a)Calculate the amount ( w ) of work produced on the system in terms of P, P(i), V, T(i) 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 final 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(i) to p = 2 p(i).(e)Compare T with T(rev), i.e., find out whether T(rev)< T , or it is the other wayaround. Provide a physical interpretation.

Explanation / Answer

(1)- W = 2PV + nRT

PV = nRT

(b) = V^2 = 2nRT

T> T rev

Pressure-volume work, (or PV work) occurs when the volume, V of a system changes. PV work is often measured in units of litre-atmospheres , where 1L

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