JEE Advanced · Physics · 12. Thermal Properties

A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat $=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$ ) of mass $\mathrm{m}$ gram is at $-5^{\circ} \mathrm{C}$ at atmospheric pressure. It is given $420 \mathrm{~J}$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 \mathrm{~g}$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is

Verified Solution

Answer & Solution

Correct Answer

(D) 8

Step-by-step Solution

Detailed explanation

Language of question is slightly wrong. As heat capacity and specific heat are two different physical quantities. Unit $\mathrm{J}-\mathrm{kg}^{-1} \cdot{ }^{\circ} \mathrm{C}^{-1}$. The heat capacity given in the question is really the specific heat. Now applying the heat exchange equation.
$
\begin{array}{r}
420=\left(m \times 10^{-3}\right)(2100)(5)+\left(1 \times 10^{-3}\right) \\
\left(3.36 \times 10^5\right)
\end{array}
$
Solving this equation we get,
$
m=8 \mathrm{~g}
$
$\therefore$ The correct answer is 8 .

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

A series LCR circuit is connected to a

45 \sin (ω t)

Volt source. The resonant angular frequency of the circuit is

10^{5} rad s^{- 1}

and current amplitude at resonance is

I_{0}

. When the angular frequency of the source is

ω = 8 \times 10^{4} rad s^{- 1}

, the current amplitude in the circuit is

0.05 I_{0}

. If

L = 50 mH

, match each entry in List-

I

with an appropriate value from List-

II

and choose the correct option.

	List- $I$		List- $II$
$P$	$I_{0}$ in $mA$	$1$	$44.4$
$Q$	The quality factor of the circuit	$2$	$18$
$R$	The bandwidth of the circuit in $rad s^{- 1}$	$3$	$400$
$S$	The peak power dissipated at resonance in Watt	$4$	$2250$
		$5$	$500$

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