JEE Mains · Physics · STD 11 - Kinetic theory of gases
- JEE Mains 2023
- Medium
- MCQ
Given below are two statements: Statements \(I:\) The temperature of a gas is \(-73^{\circ}\,C\). When the gas is heated to \(527^{\circ}\,C\), the root mean square speed of the molecules is doubled. Statement \(II:\) The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below :
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) Statement \(I\) is true but Statement \(II\) is false
Step-by-step Solution
Detailed explanation
Statement\(-I\)
\(T _1=-73^{\circ}\,C =200\,K\)
\(T _2=527^{\circ}\,C =800\,K\)
\(\frac{ V _1}{ V _2}=\frac{\sqrt{\frac{3 RT _1}{ M }}}{\sqrt{\frac{3 RT _2}{ M }}}=\sqrt{\frac{ T _1}{ T _2}}\)
\(=\sqrt{\frac{200}{800}}=\frac{1}{2}\)
\(V _2=2 V _1 \text { (True) }\)
Statement\(-II\)
\(PV = nRT\)
Translational \(KE =\frac{3}{2} nRT\) (False)
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