$$1$$ mole of a monoatomic gas at temperature $$T0$$ expand slowly according to the law $$P2$$ is proportional to T . Its final temperature is $$2T0$$, then heat supplied to the gas is

Question

$$1$$ mole of a monoatomic gas at temperature $$T0$$ expand slowly according to the law  $$P2$$  is proportional to  T . Its final temperature is $$2T0$$, then heat supplied to the gas is

Infinity Learn · Accepted Answer

Given ,Number of $$moles=1$$ moleTemperature $$=T0From$$ $$QuestionP2$$∝T⇒$$P=cT$$  ,  c is constant∴$$dPP=12dTT$$...$$.1$$ $$PV=RT$$….(2)⇒$$PdV+VdP=RdT$$⇒$$PdV=RdT$$−$$VdP=RdT$$−RT⋅$$dPP=RdT$$−$$RT2dTT($$ by using (1))=RdT2$$∴∫$$T02T0$$ $$PdV=$$∫$$T02T0$$ $$RdT2=RT02$$ From first law of $$thermodynamicsQ=$$Δ$$U+W=nCV$$Δ$$T+$$∫$$PdV=fnRT02+RT02=3(1)R2T0+RT02=2RT0$$                                                          Therefore, the correct answer is $$(D).

1 mole of a monoatomic gas at temperature $T_{0}$ expand slowly according to the law $P^{2}$ is proportional to T . Its final temperature is $2 T_{0},$ then heat supplied to the gas is

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1 mole of a monoatomic gas at temperature T0 expand slowly according to the law P2 is proportional to T . Its final temperature is 2T0, then heat supplied to the gas is

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1 mole of a monoatomic gas at temperature $T_{0}$ expand slowly according to the law $P^{2}$ is proportional to T . Its final temperature is $2 T_{0},$ then heat supplied to the gas is