A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_{1} = 10^{5} P a$ and volume $V_{i} = 10^{- 3} m^{3}$ changes to final state at $P_{f} = \frac{1}{32} \times 10^{5} p a & V_{f} = 8 \times 10^{- 3} m^{3}$ in an adiabatic quasi-static process, such that $P^{3} V^{5} =$ constant. Consider another thermodynamic process that brings the system form the same initial state to the same final state in two steps: an isobaric expansion at $P_{i}$ followed by an isochoric (is volumetric) process at volume $V_{f}$ . The amount of heat supplied to the system in the two-step process is approximately

Question

Infinity Learn · Accepted Answer

For adiabatic $$processP3V5=consntPV5/3=consntr=5/3For$$ process ACΔ$$Q1=nCp$$Δ$$T=n52R$$ΔT         $$=52P$$ΔVΔ$$Q1=17.5$$×$$102J=1750JFor$$ process  CDΔ$$Q2=nCv$$Δ$$T=n(32R)=32V$$ΔPΔ$$Q2=3/2$$×$$8$$×$$10$$−$$3$$×$$($$−$$1+132)$$×$$105$$Δ$$Q2=$$−$$11.625$$×$$102$$Δ$$Qnet=1750$$−$$1162=588J$$

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