If 250 moles of gas are compressed to 0.75 of an original volume at a constant temperature or 295 K, how much heat must have gone into the environment?
Answer
a. 176 kJ.
b. 205 kJ.
c. 112 kJ.
d. 122 kJ.
To determine the amount of heat that must have gone into the environment during this process, we can use the ideal gas law and the relationship between pressure, volume, and temperature.
The ideal gas law is given by the equation PV = nRT, where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant, and
T is the temperature of the gas.
First, let's determine the initial volume of the gas. We know that 250 moles of gas were compressed, but we need to find the initial volume at this temperature. We can rearrange the ideal gas law to solve for the initial volume:
V₁ = (n₁RT) / P₁
Where:
V₁ is the initial volume of the gas,
n₁ is the initial number of moles of gas (250 moles),
R is the ideal gas constant (8.314 J/(mol·K)),
T is the temperature of the gas (295 K), and
P₁ is the initial pressure of the gas (which is constant and not given in the question).
The final volume of the gas is given as 0.75 of the original volume, so we can calculate the final volume (V₂) as:
V₂ = 0.75 * V₁
Next, let's determine the change in volume (ΔV):
ΔV = V₂ - V₁
Now, we can calculate the work done on the gas during compression using the formula:
Work = -P₁ * ΔV
Since the process is done at a constant temperature, the work done on the gas is equal to the heat absorbed by the surroundings. Therefore, the amount of heat that must have gone into the environment is given by:
Heat = -Work
Now that you have the equation, you can substitute the values and solve for the answer.