Question

An adiabatic vessel of total volume V is divided into two equal parts by a conducting separator. The separator is fixed in this position. The part on the left contains one mole of an ideal gas (U = 1.5 nRT) and the part on the right contains two moles of the same gas. Initially, the pressure on each side is p. The system is left for sufficient time so that a steady state is reached. Find (a) the work done by the gas in the left part during the process, (b) the temperature on the two sides in the beginning, (c) the final common temperature reached by the gases, (d) the heat given to the gas in the right part and (e) the increase in the internal energy of the gas in the left part.

Answer 1

(a) As the conducting wall is fixed the work done by the gas on the left part during the process is Zero.

(b) For left side 

For right side

 Let initial Temperature = T₂
Pressure = P
Volume = V
No. of moles = n(1mole)
Let initial Temperature = T₁

(c) Let the final Temperature = T
Final Pressure = R
No. of mole = 1mole + 2moles = 3moles

Comments

your (e) part is not the correct way to answer this

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As we know that, work done (dW) by the gas is zero. So the given equation is written in that way.