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(B) For an ideal gas at constant pressure,the heat supplied is $Q = n C_P \Delta T$ and the work done is $W = n R \Delta T$.Given $Q = x$ and $W = x/3

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$4$

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(B) For an ideal gas at constant pressure,the heat supplied is $Q = n C_P \Delta T$ and the work done is $W = n R \Delta T$.Given $Q = x$ and $W = x/3$,we have the ratio $\frac{W}{Q} = \frac{n R \Delta T}{n C_P \Delta T} = \frac{R}{C_P} = \frac{x/3}{x} = \frac{1}{3}$.We know that $C_P = C_V + R = \frac{f}{2}R + R = R(\frac{f}{2} + 1) = R(\frac{f+2}{2})$.Substituting this into the ratio: $\frac{R}{R(\frac{f+2}{2})} = \frac{2}{f+2} = \frac{1}{3}$.Solving for $f$: $f+2 = 6$,which gives $f = 4$.

When $x$ amount of heat is given to a gas at constant pressure,it performs $x/3$ amount of work. The average number of degrees of freedom per molecule is

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