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Two different masses \mathrm{m} and \mathrm{3m} of an ideal gas are heated separately in a vessel of constant volume. The pressure \mathrm{p} and absolute temperature \mathrm{T} graphs for these two cases are shown in the figure as \mathrm{A} and \mathrm{B}. The ratio of slopes of curves \mathrm{B} to \mathrm{A} is


 

Option: 1

3: 1


Option: 2

1: 3


Option: 3

9: 1


Option: 4

1: 9


Answers (1)

best_answer

For a gas, \mathrm{p V=n R T=\frac{m}{M} R T}

Slope of graph \mathrm{A_{1}\left(\frac{p}{T}\right)=\frac{m}{M} \frac{R}{V}}\quad \ldots(i)



Similarly, slope of graph \mathrm{B, \frac{p}{T}=\frac{3 m}{M} \frac{R}{V}}\quad \ldots(ii)

\mathrm{\therefore \quad \frac{\text { Slope of curve } B}{\text { Slope of curve } A}=\frac{\frac{3 m}{M} \frac{R}{V}}{\frac{m}{M} \frac{R}{V}}=\frac{3}{1}}

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