A piece of ice (heat capacity and latent heat ) of mass grams is at at atmospheric pressure. It is given of heat so that the ice starts melting. [2010]

Question

A piece of ice (heat capacity $= 2100 J {kg}^{- 1} ° C^{- 1}$ and latent heat $= 3.36 \times 10^{5} J {kg}^{- 1}$ ) of mass $m$ grams is at $- 5 ° C$ at atmospheric pressure. It is given $420 J$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 gm$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is [2010]

Smart Achievers · Accepted Answer

(8)

As there is no other heat exchange in this process, So, Heat supplied = Heat used in converting $m$ grams of ice from $- 5 ° C$ to $0 ° C$ + Heat used in converting 1 gram of ice at $0 ° C$ to water at $0 ° C$

or, $420 = m c Δ θ + m l$

$\Rightarrow 420 = m \times \frac{2100}{1000} \times 5 + \frac{1 \times 3.36 \times 10^{5}}{1000}$

$\Rightarrow 420 = m \times 10.5 + 336$

$∴$ $m = \frac{84}{10.5} = 8 g$

Solution

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Solution

Ans. (8) As there is no other heat exchange in this process, So, Heat supplied = Heat used in converting m grams of ice from -5°C to 0°C + Heat used in converting 1 gram of ice at 0°C to water at 0°C or, 420=mcΔθ+ml ⇒420=m×21001000×5+1×3.36×1051000 ⇒420=m×10.5+336 ∴ m=8410.5=8 g

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