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  • Thermodynamic process is shown below on a  diagram for one mole of an ideal gas. If <img alt="V_{2}=2V_{1}" src="https://entrancecorner.codecogs.com/gif.latex?V_%7B2%7D%

Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V_{2}=2V_{1} then the ratio of temperature \frac{T_{2}}{T_{1}} is :
       
Option: 1 \frac{1}{2}
Option: 2 2
Option: 3 \sqrt{2}  
Option: 4 \frac{1}{\sqrt{2}}

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\begin{array}{l} \mathrm{PV}^{1 / 2}=\mathrm{c} \\ \text{Using } PV=nRT \\ \Rightarrow \frac{\mathrm{nRT}}{\mathrm{V}} *\mathrm{V}^{1 / 2}=\mathrm{c} \\ \Rightarrow \mathrm{T}=\mathrm{c}^{1} \mathrm{~V}^{1 / 2} \\ \Rightarrow \frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\left(\frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}\right)^{1 / 2}=\left(\frac{2 \mathrm{~V}_{1}}{\mathrm{~V}_{1}}\right)^{1 / 2} \\ \Rightarrow \frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\sqrt{2} \end{array}

 

 

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Deependra Verma

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