The variation of volume $V$ , with the temperature $T$ , keeping pressure constant is called the coefficient of thermal expansion ( $α$ ) of a gas ie., $α = \frac{1}{V} {(\frac{\partial V}{\partial T})}_{P}$
For an ideal gas $α$ is equal to :

T

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1 / T

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P

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1 / P

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Solution

The correct option is B $1 / T$
For $n$ moles of an ideal gas $P V = n R T$

or $V = n \frac{R T}{P}$

Differentiating with respect to $T$ at cosntant $P$ , we have
${(\frac{\partial V}{ð T})}_{P} = \frac{n R}{P} = \frac{V}{T}$

$α = \frac{1}{V} \times \frac{V}{T} = \frac{1}{T}$

Option B is correct.

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β = \frac{{(\frac{p a r t i a l V}{\partial P})}_{T}}{V}

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Q. Assertion :

C_{P} - C_{V} = R

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You might be familiar with the ideal gas equation from Chemistry, which relates the pressure and volume of an ideal gas with temperature as: $P V$ = $n R T$ , where $n R$ is a constant. You are given a closed metal container of volume $V$ , filled with a gas kept at a temperature $T$ , and pressure $P$ . If $γ$ is the coefficient of volume expansion for the gas, what is the pressure after the temperature is increased by $Δ T$ ?