A monatomic gas of n moles undergoes a cyclic process ABCDA as shown in figure. Process AB is isobaric, BC is adiabatic, CD is isochoric and DA is isothermal. The maximum and minimum temperature in the cycle are $$4T0$$ and $$T0$$ respectively. Then

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Process DA is isothermal⇒ $$TD=TAFurther$$ T∝PVFrom the graph we can see that $$(PV)C$$>$$(PV)D$$⇒ TC>TDFurther process BC is an adiabatic expansion. So, TD>TC Therefore, maximum temperature is at B and minimum temperature at D or A. Hence,$$TB=4T0$$ and $$TD=TA=T0In$$ process CD:         $$W=0$$⇒ $$Q=$$ΔU                 $${$$∵ of FLTD $$}Volume$$ of the gas is constant and pressure is decreasing. Therefore, temperature and hence, internal energy will decrease ie., Q is negative or heat is released by the gas in the process CD.In process AB:$$Q=nCp$$ΔT           $${$$ process is isobaric $$}Pressure$$ is constant and volume is increasing. Therefore, temperature will also increase or Q is positive. Thus, heat is supplied to the gas only in process ABand $$Q=n5R2TB$$−TA⇒ $$Q=n5R24T0$$−$$T0=152nRT0$$

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