n moles of an ideal monoatomic gas undergoes a process from $$1$$ →$$4$$ as shown in the figure. $$T1=500$$ K, $$T4=200$$ K, $$P1=105$$ Pa and $$P2=4$$×$$105Pa$$. In state $$3$$, $$3V3=V1$$. The change in internal energy from state $$3$$ to state $$4$$ is x Joules. The value of ‘x’ is (Take$$ no. of moles n $$=$$ $$1/R$$, where R $$=$$ gas $$constant)

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n moles of an ideal monoatomic gas undergoes a process from $$1$$ →$$4$$ as shown in the figure. $$T1=500$$ K,  $$T4=200$$ K, $$P1=105$$  Pa and $$P2=4$$×$$105Pa$$. In state $$3$$, $$3V3=V1$$. The change in internal energy from state $$3$$ to state $$4$$ is x Joules. The value of ‘x’ is (Take$$ no. of moles n $$=$$ $$1/R$$, where R $$=$$ gas $$constant)

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P−$$4$$×$$105T$$−$$500=$$−$$3$$×$$105$$−$$300$$⇒$$P=103T$$−$$105$$⇒$$nRTV=103T$$−$$105As$$  $$n=1R$$​⇒$$1V=103$$−$$105T$$  straight line from $$2$$ to $$4$$​At point $$1$$ , $$V1=nRT1P1=500105m3$$ ​Given : $$3V3=V1$$​⇒$$V3=V13=5003$$×$$105m3At$$ point $$3$$,$$1V3=103$$−$$105T3$$​⇒$$3$$×$$105500=1000$$−$$105T3$$​⇒$$600=1000-105T3$$⇒$$T3=250K$$​Change in internal energy from state $$3$$ to state $$4$$ , △$$U=nCVT4$$−$$T3=32$$×$$200$$−$$250$$ $$=$$−$$75J$$

n moles of an ideal monoatomic gas undergoes a process from 1 →4 as shown in the figure. T1=500 K, T4=200 K, P1=105 Pa and P2=4×105Pa. In state 3, 3V3=V1. The change in internal energy from state 3 to state 4 is x Joules. The value of ‘x’ is (Take no. of moles n = 1/R, where R = gas constant)

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