MHT CET · Physics · Thermodynamics
A gas expands in such a way that its pressure and volume satisfy the condition \(\mathrm{PV}^2=\) constant. Then the temperature of the gas
- A will decrease.
- B will increase.
- C will not change.
- D may increase or decrease depending upon the values of pressure and volume.
Answer & Solution
Correct Answer
(A) will decrease.
Step-by-step Solution
Detailed explanation
Ideal gas equation is, \(\mathrm{PV}=\mathrm{nRT}\)
\(\begin{aligned}
\therefore \quad & P=\frac{n R T}{V} \\
& \text { Since, } \\
& P V^2=\text { constant } \\
& \left(\frac{n R T}{V}\right) V^2=\text { constant } \\
\therefore \quad & T V=\text { constant } \\
\quad & T \propto \frac{1}{V}
\end{aligned}\)
With expansion of gas, temperature decreases.
\(\begin{aligned}
\therefore \quad & P=\frac{n R T}{V} \\
& \text { Since, } \\
& P V^2=\text { constant } \\
& \left(\frac{n R T}{V}\right) V^2=\text { constant } \\
\therefore \quad & T V=\text { constant } \\
\quad & T \propto \frac{1}{V}
\end{aligned}\)
With expansion of gas, temperature decreases.
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