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  • A balloon is filled with a mixture of ideal gases. The pressure P in the balloon is related to the volume Vas <img alt="\mathrm{P V^{2 / 3}=k}" src="https://entrancecorner.oncodecogs.com/gif.l

A balloon is filled with a mixture of ideal gases. The pressure P in the balloon is related to the volume Vas \mathrm{P V^{2 / 3}=k}, where k is a constant. If T is the temperature of the mixture, volume V is proportional to

Option: 1

T


Option: 2

\mathrm{T^2}


Option: 3

\mathrm{T^3}


Option: 4

\mathrm{T^4}


Answers (1)

best_answer

\mathrm{P V^{2 / 3}=k}             [1]

\mathrm{\text { Equation of state is } P V=n R T \Rightarrow P=\frac{n R T}{V}}

Using this in Eq. (1) we get

\mathrm{\frac{n R T}{V} \times V^{2 / 3}=k}

\mathrm{\text { Or } T V^{-1 / 3}=\frac{k}{n R}=\text { constant }}

\mathrm{\text { Hence } V \propto T^3}

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Gunjita

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