The variation of volume V, with temperature T, keeping pressure constant is called the coefficient of thermal expansion i.e. $\alpha=\dfrac{1}{V}\left(\dfrac{\partial V}{\partial T}\right)_P$. For an ideal gas $\alpha$ is equal to (a) T (b) $\dfrac{1}{T}$ (c) P (d) none of these

The variation of volume V, with temperature T, keeping pressure constant is called the coefficient of thermal

Choose the Best Answer · Q18

\alpha=\dfrac{1}{V}\left(\dfrac{\partial V}{\partial T}\right)_P

(a) T

(b)

\dfrac{1}{T}

(d) none of these

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Step 1. For an ideal gas, $V=\dfrac{nRT}{P}$ . Differentiating with respect to T at constant P: $\left(\dfrac{\partial V}{\partial T}\right)_P=\dfrac{nR}{P}$ .

Step 2. Since $\dfrac{nR}{P}=\dfrac{V}{T}$ (rearranging the ideal gas equation), $\left(\dfrac{\partial V}{\partial T}\right)_P=\dfrac{V}{T}$ . …

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Q.The variation of volume V, with temperature T, keeping pressure constant is called the coefficient of thermal expansion i.e. $\alpha=\dfrac{1}{V}\left(\dfrac{\partial V}{\partial T}\right)_P$ . For an ideal gas $\alpha$ is equal to

Concept understanding — Charles's Law (Volume-Temperature Relationship)

Q.The variation of volume V, with temperature T, keeping pressure constant is called the coefficient of thermal expansion i.e. α=1V(∂V∂T)P\alpha=\dfrac{1}{V}\left(\dfrac{\partial V}{\partial T}\right)_Pα=V1​(∂T∂V​)P​. For an ideal gas α\alphaα is equal to

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Q.The variation of volume V, with temperature T, keeping pressure constant is called the coefficient of thermal expansion i.e. $\alpha=\dfrac{1}{V}\left(\dfrac{\partial V}{\partial T}\right)_P$ . For an ideal gas $\alpha$ is equal to

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