Question

100 g of Ice at -10°C is added into a

liquid juice at 20°c . The temperature of Juice
dropped to l0°c after all the Ice has melted.
Calculate the mass of the Juice responsible
for metting an Ice​

Answer 1

The mass of the juice responsible for melting the ice is 949.043 grams.

Step-by-step explanation:

By the First Law of Thermodynamics, we understand that juice releases heat to the ice, which turns into water under the assumption that interactions between the ice-juice system and surroundings are negligible and energy processes are done in steady-state. Since juice is done with water, its specific heat will be taken as of the water. The process is described by the following formula:

`m_(i) \cdot [c_(i)\cdot (T_(1)-T_(2)) - L_(f) + c_(w)\cdot (T_(2)-T_(3))] + m_(w) \cdot c_(w)\cdot (T_(4)-T_(3)) = 0` (1)

Where:

`m_(i)` - Mass of ice, in grams.

`m_(w)` - Mass of the juice, in grams.

`c_(i)` - Specific heat of ice, in joules per gram-degree Celsius.

`c_(w)` - Specific heat of water, in joules per gram-degree Celsius.

`L_(f)` - Latent heat of fusion, in joules per gram.

`T_(1)` - Initial temperature of ice, in degrees Celsius.

`T_(2)` - Melting point of water, in degrees Celsius.

`T_(3)` - Final temperature of the ice-juice system, in degrees Celsius.

`T_(4)` - Initial temperature of the juice, in degrees Celsius.

If we know that
`m_(i) = 100\,g`,
`c_(i) = 2.090\,(J)/(g\cdot ^(\circ)C)`,
`c_(w) = 4.18\,(J)/(g\cdot ^(\circ)C)`,
`L_(f) = 334\,(J)/(g)`,
`T_(1) = -10\,^(\circ)C`,
`T_(2) = 0\,^(\circ)C`,
`T_(3) = 10\,^(\circ)C` and
`T_(4) = 20\,^(\circ)C`, then the mass of the juice is:

`m_(w) = (m_(i)\cdot [c_(i)\cdot (T_(1)-T_(2)) - L_(f) + c_(w)\cdot (T_(2)-T_(3))])/(c_(w) \cdot (T_(3)-T_(4)))`

`m_(w) = ((100\,g)\cdot \left[\left(2.090\,(J)/(g\cdot ^(\circ)C) \right)\cdot (-10\,^(\circ)C) - 334\,(J)/(g) +\left(4.18\,(J)/(g\cdot ^(\circ)C) \right)\cdot (-10\,^(\circ)C) \right])/(\left(4.180\,(J)/(g\cdot ^(\circ)C) \right)\cdot (-10\,^(\circ)C))`

`m_(w) = 949.043\,g`

The mass of the juice responsible for melting the ice is 949.043 grams.