A piece of ice (heat capacity = 2100J kg^(-1 @)C ^-1 and latent heat = 3.36 xx 10^5 J kg^-1) of mass m gram is at -5^@C at atmospheric pressure. It isgiven 420 J of heat so that the ice starts melting. Finally when the ..........?

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

May 4, 2018

Refer to Explanation

Explanation:

Thermal energy absorbed to heat up the ice to ${0}^{\circ} C$:
$Q = m c \Delta \theta$
$Q = \frac{m}{1000} \cdot 2100 \cdot \left[0 - \left(- 5\right)\right]$
$Q = \left(10.5 m\right) J$

Thermal energy absorbed to melt 1g of ice:
$Q = m {l}_{v}$
$Q = \frac{1}{1000} \cdot 3.36 \times {10}^{5}$
$Q = 336 J$

$\left(10.5 m\right) J + 336 J = 420 J$
$\therefore m = 8 g$