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  • During an experiment, an ideal gas is found to obey a condition <img alt="\mathrm{p^{2} / \rho= constant}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bp%5E%7B2%7D%20/%20%5Crho%

During an experiment, an ideal gas is found to obey a condition \mathrm{p^{2} / \rho= constant}. The gas is initially at temperature T, pressure \mathrm{p} and density \mathrm{\rho}.The gas expands such that density changes to \mathrm{\rho / 2} and

Option: 1

the pressure of the gas changes to \sqrt{2} \mathrm{P}


Option: 2

 the pressure of the gas changes to \sqrt{3} T


Option: 3

 the graph of the above process on the P-T graph is parabola


Option: 4

the graph of the above process on the P-T graph is hyperbola


Answers (1)

best_answer

\mathrm{\frac{\mathrm{P}^{2}}{\rho}=\text { constant }}

\mathrm{\Rightarrow \quad \frac{\mathrm{P}^{2}}{\rho}=\frac{\mathrm{P}_{1}^{2}}{\rho} \cdot 2}

\mathrm{\Rightarrow \quad \mathrm{P}_{1}=\frac{\mathrm{P}}{\sqrt{2}}}
\mathrm{\frac{\mathrm{P}^{2}}{\rho}= constant}
\mathrm{\Rightarrow \quad \frac{\rho^{2} T^{2}}{\rho}= constant}\quad [\text{For ideal gas }\mathrm{P}=\rho \mathrm{RT} ]
        
\mathrm{\therefore \quad \rho \mathrm{T}^{2}= constant}

\mathrm{\therefore \quad \rho \mathrm{T}^{2}=\frac{\rho}{2} \mathrm{~T}_{1}^{2}}
\mathrm{\Rightarrow \quad \mathrm{T}_{1}=\sqrt{2} \mathrm{~T}}
\mathrm{\frac{\mathrm{P}^{2}}{\rho}= constant}
\mathrm{\Rightarrow \quad \mathrm{P}^{2} \frac{\mathrm{T}}{\mathrm{P}}= constant}
\mathrm{\therefore \quad \mathrm{PT}= constant}

\mathrm{\Rightarrow Graph of process on P-T graph is hyperbola.

 

Posted by

Deependra Verma

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