The density of a liquid at 0^∘ C is ρ0. The density of liquid at 0^∘ C is : [volume expansion of

Name: Problem 30, Chapter 15: Arihant AIEEE Physics
Uploaded: 2021-09-19T14:47:11-08:00
Duration: 1 min 28 s
Channel: Ajay Singhal
Description: The density of a liquid at 0^∘ C is ρ0. The density of liquid at 0^∘ C is : [volume expansion of liquid is γ] (a) (ρ0)/([1+γ(θ2-θ1)]) (b) ρ0[1+γ(θ2-θ1)] (c) ρ0[1+γθ2] (d) none of these

step 1 Hello students in this question we have given that the density of the liquid at the theta 1 degr

Question

The density of a liquid at $0^{\circ} \mathrm{C}$ is $\rho_{0}$. The density of liquid at $0^{\circ} \mathrm{C}$ is : [volume expansion of liquid is $\gamma$ ] (a) $\frac{\rho_{0}}{\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]}$ (b) $\rho_{0}\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]$ (c) $\rho_{0}\left[1+\gamma \theta_{2}\right]$ (d) none of these

   The density of a liquid at $0^{\circ} \mathrm{C}$ is $\rho_{0}$. The density of liquid at $0^{\circ} \mathrm{C}$ is : [volume expansion of liquid is $\gamma$ ]
(a) $\frac{\rho_{0}}{\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]}$
(b) $\rho_{0}\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]$
(c) $\rho_{0}\left[1+\gamma \theta_{2}\right]$
(d) none of these

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 15, Problem 30

Instant Answer

Solved by Expert Ajay Singhal

09/19/2021

Step 1

So, we can write the density at $0^{\circ} \mathrm{C}$ as $\rho_{0} = \frac{m}{V_{0}}$, where $m$ is the mass and $V_{0}$ is the volume at $0^{\circ} \mathrm{C}$. Show more…

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The density of a liquid at $0^{\circ} \mathrm{C}$ is $\rho_{0}$. The density of liquid at $0^{\circ} \mathrm{C}$ is : [volume expansion of liquid is $\gamma$ ] (a) $\frac{\rho_{0}}{\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]}$ (b) $\rho_{0}\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]$ (c) $\rho_{0}\left[1+\gamma \theta_{2}\right]$ (d) none of these

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Key Concepts

Relationship Between Density and Volume Change

Since density is inversely proportional to volume, when a liquid experiences thermal expansion by a factor of (1 + ??T), its density decreases to ? = ?? / (1 + ??T). This relationship is essential to understanding how liquids behave under temperature variations.

Conservation of Mass

In any thermal process affecting a liquid, the mass remains constant. This principle means that any change in volume directly affects density, since density is the mass divided by the volume.

Density

Density is defined as the mass per unit volume of a substance. It is a fundamental property that can change with temperature due to the corresponding change in volume, even though the mass remains constant.

Volume Expansion Coefficient

The volume expansion coefficient (?) measures the fractional change in volume per unit change in temperature. It is used to determine how much a liquid will expand or contract when the temperature is varied.

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