To raise the temperature of a certain mass of gas by $$500C$$ at a constant pressure, $$160$$ calories of heat is required. When the same mass of gas is cooled by $$1000C$$ at constant volume, $$240$$ calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume$$ gas to $$ideal)?

Question

To raise the temperature of a certain mass of gas by $$500C$$ at a constant pressure, $$160$$ calories of heat is required. When the same mass of gas is cooled by $$1000C$$ at constant volume, $$240$$ calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume$$ gas to $$ideal)?

Infinity Learn · Accepted Answer

At constant pressure  $$dQ=mcpdT$$ $$160=mcP50At$$ constant $$volumedQ=mcVdT240=mcV(100)$$⇒⇒$$cP(50)cv(100)=160240$$γ$$2=23$$∵γ$$=cPcv=CPCv$$γ$$=43f=2$$γ$$-1=243-1=6$$

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