An ideal gas whose adiabatic exponent equals to $$75$$ is expanded according to the law P $$=$$ $$2V$$.The initial volume of the gas is equal to Vo $$=$$ $$1$$ unit. As a result of expansion the volume increases $$4$$ times. $$(Take$$ R $$=$$ $$units)Now$$ much the given columns and select the correct option from the codes given below.Codes

Question

An ideal gas whose adiabatic exponent equals to $$75$$ is expanded according to the law P $$=$$ $$2V$$.The initial volume of the gas is equal to Vo $$=$$ $$1$$ unit. As a result of expansion the volume increases $$4$$ times. $$(Take$$ R $$=$$ $$units)Now$$ much the given columns and select the correct option from the codes given below.Codes

Infinity Learn · Accepted Answer

W $$=$$ ∫ PdV  $$=$$ ∫$$V04V02VdV$$ $$=$$ (V2)V04V0$$ $$=$$ $$15V02$$ $$=$$ $$15$$ unitsFrom PV $$=$$ nRT, $$2V2$$ $$=$$ nRT⇒$$2(V22-V12) $$=$$  $$nR($$∆$$T)$$    nR∆T $$=$$ $$30V02$$∆U $$=$$ nCv∆T $$=$$ nRγ$$-1$$∆T $$=$$ $$30V02$$γ$$-1$$ $$=$$ $$30(1)275-1$$ $$=$$ $$30$$ $$2(5)$$        $$=$$ $$75$$ unitsQ $$=$$ W $$+$$ ∆U $$=$$ $$15+30$$ $$=$$ $$45$$ unitsMolar heat capacity:C $$=$$ $$Cv+R1-x$$ $$=$$ $$52R+R1-(-1)$$ $$=$$ $$52R+R2$$ $$=$$ $$3R$$    $$=$$ $$3$$ ×$$253$$ $$=$$ $$25$$ units

	Column-I		Column-II
i.	Work done by the gas	p.	25 units
ii.	Increment in internal energy of the gas	q.	45 units
iii.	Heat supplied to the gas	r.	75 units
iv.	Molar heat capacity of the gas in the process	s.	15 units
		t.	55 units

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