Jawaban:

The heat that must be eliminated from the system is 1521.2 J.

Penjelasan:

To solve this problem, we need to use the ideal gas law, which states that the volume of a gas is directly proportional to its temperature (measured in Kelvins) and inversely proportional to its pressure. The ideal gas law is given by:

PV = nRT

where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, R is the universal gas constant, and T is the temperature of the gas in Kelvins.

In this case, we are given that the pressure of the gas is 6 atmospheres, the number of moles of the gas is 8, and the gas constant is 8.314 J/mol.K. The initial temperature of the gas is not given, but we are told that the gas is being compressed to a final temperature of -150 degrees Celsius. To use the ideal gas law, we need to convert this temperature to Kelvins by adding 273.15 to the temperature in Celsius:

Tfinal (in Kelvins) = -150 + 273.15 = 123.15 K

We can now use the ideal gas law to calculate the final volume of the gas:

Vfinal = (nRT) / P = (8 * 8.314 * 123.15) / 6 = 205.7 liters

To determine the heat that must be eliminated from the system, we can use the equation for isobaric heat capacity, which is given by:

q = Cpm * (Tfinal - Tinitial)

where q is the heat that must be eliminated from the system, Cpm is the heat capacity of the gas at constant pressure, Tfinal is the final temperature of the gas, and Tinitial is the initial temperature of the gas. In this case, we are given that Cpm is 22 J/mol.K. We need to determine the initial temperature of the gas in order to calculate the heat that must be eliminated from the system.

To do this, we can use the ideal gas law to solve for the initial volume of the gas, given that the initial pressure and number of moles of the gas are known:

Vinitial = (nRT) / P = (8 * 8.314 * Tinitial) / 6

Substituting the known values, we get:

Vinitial = (8 * 8.314 * Tinitial) / 6 = 50 liters

Solving for Tinitial, we find that the initial temperature of the gas is approximately -217.6 degrees Celsius. Converting this temperature to Kelvins, we find that the initial temperature of the gas is 55.55 K.

Now that we know the initial and final temperatures of the gas, we can use the equation for isobaric heat capacity to calculate the heat that must be eliminated from the system:

q = Cpm * (Tfinal - Tinitial) = 22 * (123.15 - 55.55) = 22 * 67.6 = 1521.2 J

Therefore, the volume of the gas after compression is 205.7 liters, and the heat that must be eliminated from the system is 1521.2 J.