Physics - Heat & Thermo Question with Solution | TestHub

PhysicsHeat & ThermoDifferent processesHard2 minPYQ_2023

PhysicsHardsingle choice

The pressure $(P)$ and temperature $(T)$ relationship of an ideal gas obeys the equation $P T^{2} =$ constant. The volume expansion coefficient of the gas will be :

Options:

Answer:

Solution:

Given here,

$P T^{2} =$ constant $. . . (1)$

Using ideal gas equation,

$P V = n R T$

We have, $P = \frac{n R T}{V}$

Putting in equation $(1)$ ,

$P T^{2} = \frac{n R T}{V} \times T^{2} =$ constant

$\Rightarrow T^{3} = K V . . . (2)$

Differentiating the equation with respect to $T$ ,

So, $\frac{d}{d T} (K V) = 3 T^{2}$

$\Rightarrow \frac{K d V}{d T} = 3 T^{2}$

$\Rightarrow d V = \frac{3 T^{2}}{K} d T$

$\Rightarrow γ V = \frac{3 T^{2}}{K} (as d V = γ V d T)$

$\Rightarrow γ = \frac{3 T^{2}}{K V} = \frac{3 T^{2}}{T^{3}} = \frac{3}{T}$

Stream:JEESubject:PhysicsTopic:Heat & ThermoSubtopic:Different processes

⏱ 2mℹ️ Source: PYQ_2023

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