Question

If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature

• A. Is doubled
• B. Becomes one-fourth
• C. Remains constant
• D. Become four times

Answer 1

Answer: (B)

Becomes one-fourth

Answer 2

According to ideal gas law

$\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}orT_{2} = T_{1}\frac{P_{2}V_{2}}{P_{1}V_{1}}$

Here, $P_{1} = P,V_{1} = V,T_{1} = T$

$P_{2} = \frac{P}{2},V_{2} = \frac{V}{2},T_{2} = ?$

$\therefore T_{2} = \frac{T\left( \frac{P}{2} \right)\left( \frac{V}{2} \right)}{PV}$

$T_{2} = \frac{T}{4}$