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

Detailed Solution

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