You wish to cool a 1.83 kg block of tin initially at 88.0°C to a temperature of 57.0°C by placing it in a container of kerosene initially at 24.0°C. Determine the volume (in L) of the liquid needed in order to accomplish this task without boiling. The density and specific heat of kerosene are respectively 820 kg/m3 and 2,010 J/(kg · °C), and the specific heat of tin is 218 J/(kg · °C).

0.273 liters are needed to accomplish this task without boiling.

Explanation:

The minimum boiling point of kerosene is . According to this question, we need to determine the minimum volume of liquid such that heat received is entirely sensible, that is, with no phase change.

If we consider a steady state process and that energy interactions with surrounding are negligible, then we get the following formula by the Principle of Energy Conservation:

(1)

Where:

- Density of kerosene, measured in kilograms per cubic meter.

- Volume of kerosene, measured in cubic meters.

, - Specific heats of the kerosene and tin, measured in joule per kilogram-Celsius.

, - Initial temperatures of kerosene and tin, measured in degrees Celsius.

- Final temperatures of the kerosene-tin system, measured in degrees Celsius.

Please notice that the block of tin is cooled at the expense of the temperature of the kerosene until thermal equilibrium is reached.

From (1), we clear the volume of kerosene:

If we know that , , , , , and , then the volume of the liquid needed to accomplish this task without boiling is:

0.273 liters are needed to accomplish this task without boiling.

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.