Question

If there is no heat loss, the heat released by the condensation of x grams of steam at ${100}^{\circ }C$ into water at ${100}^{\circ }C$ converts y grams of ice at $0^{\circ }C$ into water at ${100}^{\circ }C$. Find the ratio of y to x.

Answer 1

Given: If there is no heat loss, the heat released by the condensation of $x$ grams of steam at ${100}^{\circ }C$ into water at ${100}^{\circ }C$ converts $y$ grams of ice at $0^{\circ }C$ into water at ${100}^{\circ }C$.

To find the ratio of y to x.

Solution:

Asper given condition,

Mass of steam, $m_s=xg$

Mass of water, $m_w=yg$

We know,Specific heat of water = $4.2J/\left(g^{\circ }C\right)$

Latent heat of fusion of ice = $334J/g$

latent heat of vaporization of water = $2260J/g$

Heat loss by $x$ gm of steam = $x\times 2260J$

Heat gain by $y$ gm of ice to become water at ${100}^{\circ }C$

$=y\times 334+y\times 4.2\times 100=y\times 334+420\times y=754\times y$

We know,

Heat gained = heat lost

Hence, $x\times 2260=754\times y⟹y:x=\frac{2260}{754}⟹y:x=3:1$