AP EAMCET · PHYSICS · Thermal Properties of Matter

A glass vessel of volume $V_{0}$ is completely filled with a liquid and its temperature is raised by $Δ T$ . What volume of the liquid will flow over, if the coefficient of linear expansion of glass is $α_{g}$ and coefficient of volume expansion of the liquid is $γ_{L}$

A $V_{o} Δ T (γ_{L} - 3 α_{g})$
B $V_{o} Δ T (3 α_{g} - γ_{L})$
C $(γ_{L} - 3 α_{g}) Δ T$
D $(3 α_{g} - γ_{L}) Δ T$

Verified Solution

Answer & Solution

Correct Answer

(A) $V_{o} Δ T (γ_{L} - 3 α_{g})$

Step-by-step Solution

Detailed explanation

Volume of the liquid overflow = Increase in the volume of the liquid − increase in the volume of the container. =V01+γL∆T-V0-V01+γg∆T-V0 =V0∆TγL-γg =V0∆TγL-3αg

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A glass vessel of volume V0 is completely filled with a liquid and its temperature is raised by ΔT. What volume of the liquid will flow over, if the coefficient of linear expansion of glass is αg and coefficient of volume expansion of the liquid is γL

Step-by-step Solution

A glass vessel of volume $V_{0}$ is completely filled with a liquid and its temperature is raised by $Δ T$ . What volume of the liquid will flow over, if the coefficient of linear expansion of glass is $α_{g}$ and coefficient of volume expansion of the liquid is $γ_{L}$