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​

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

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:

(1)

Where:

- Mass of ice, in grams.

- Mass of the juice, in grams.

- Specific heat of ice, in joules per gram-degree Celsius.

- Specific heat of water, in joules per gram-degree Celsius.

- Latent heat of fusion, in joules per gram.

- Initial temperature of ice, in degrees Celsius.

- Melting point of water, in degrees Celsius.

- Final temperature of the ice-juice system, in degrees Celsius.

- Initial temperature of the juice, in degrees Celsius.

If we know that , , , , , , and , then the mass of the juice is:

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

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west