An object kept in a large room having air temperature of \(25^{\circ} \mathrm{C}\) takes \(12\) minutes to cool from \(80^{\circ} \mathrm{C}\) to \(70^{\circ} \mathrm{C}\). The time taken to cool for the same object from \(70^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) would be nearly.....\(min\)

A \(10\)
B \(12\)
C \(20\)
D \(15\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(15\)

Step-by-step Solution

Detailed explanation

\(\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{t}}=\mathrm{K}\left(\frac{\mathrm{T}_{1}+\mathrm{T}_{2}}{2}-\mathrm{Ts}\right)\) \(\frac{80-70}{12}=\mathrm{K}\left(\frac{80+70}{2}-25\right) \ldots(1)\)

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.

Same subject

Match Column \(- I\) and Column \(- II\) and choose the correct match from the given choices.

Column \(- I\)	Column \(- II\)
\((A)\) Root mean square speed of gas molecules	\((P)\) \(\frac{1}{3} \mathrm{n} m \bar{v}^{2}\)
\((B)\) Pressure exerted by ideal gas	\((Q)\) \(\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}\)
\((C)\) Average kinetic energy of a molecule	\((R)\) \(\frac{5}{2} \mathrm{RT}\)
\((D)\) Total internal energy of \(1\) mole of a diatomic gas	\((S)\) \(\frac{3}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}\)

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