Question

$80g$ of water at ${30}^{o}C$ is poured on a large block of ice at $0^{o}C$. The mass of ice that melts is:

• A. $30g$
• B. $80g$
• C. $1600g$
• D. $150g$

Answer 1

The correct option is A $30g$

According to thermodynamics,

Heat loss by water = heat gain by ice

It is given that,

Mass of water, $m=80gm$

Specific heat of water, $s=1cal/gm{/}^{0}C$

So, heat lost by water during cooling fro ${30}^{0}C$to $0^{0}C$

$\Delta H=ms\Delta T$

$\Delta H=80\times 1\times (30-0)$

$\Delta H=2400cal........\left(1\right)$

Heat gain by ice, $m_{1}l=m_1\times 80cal/gm.....\left(2\right)$

Where, $l$ is the latent heat of fusion

$m_1$ is the mass of ice melted.

From equation (1) and (2)

$2400=80m_1$

$m_1=30g$

Hence, $30g$ of ice is melted.