The air in a cylinder of a diesel engine occupies 1.00 L at 30 degrees celsius and 1.00 atm. What is the pressure in the cylinder when the air is compressed to 0.0714 L (14:1 compression ratio) and heats to 480 degrees celsius? When the fuel explodes in the compression chamber, the temperature increases to 2,000 degrees celsius for an instant. What is the pressure of the gases in the cylinder at this instant before expansion occurs?
For this problem would I just add the two pressures (1+.0714) together? I'm pretty sure I'm completely wrong.
a.
Use (p1v1/t1) = (p2v2/t2)
p1 = 1 atm
v1 = 1 L
T1 = 30 + 27 = ?Kelvin
P2 = ?
V2 = 0.0714 L
T2 = 480 + 27 = ?Kelvin.
b part is done the same way.
To solve this problem, you need to use the ideal gas law equation, which relates the pressure (P), volume (V), temperature (T), and the number of moles of gas (n). The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = gas constant
T = temperature
In this problem, since the number of moles of gas (n) remains constant, we can rewrite the ideal gas law equation as:
P1 * V1 / T1 = P2 * V2 / T2
Where the subscripts 1 and 2 represent the initial and final states, respectively. We can use this equation to find the pressures at different states of the system.
1) First, let's calculate the pressure in the cylinder when the air is compressed to 0.0714 L and heated to 480 degrees celsius:
Given:
V1 = 1.00 L
T1 = 30 degrees celsius (convert to Kelvin by adding 273.15)
V2 = 0.0714 L
T2 = 480 degrees celsius (convert to Kelvin by adding 273.15)
Plugging in these values into the equation, we have:
P1 * 1.00 L / (30 + 273.15 K) = P2 * 0.0714 L / (480 + 273.15 K)
Simplifying the equation, we get:
P2 = P1 * (0.0714 L / 1.00 L) * (30 + 273.15 K) / (480 + 273.15 K)
2) To find the pressure of the gases in the cylinder at the instant before expansion occurs (when the fuel explodes and the temperature increases to 2000 degrees Celsius), we can use the following equation:
P1 * 1.00 L / (30 + 273.15 K) = P3 * 1.00 L / (2000 + 273.15 K)
Solving for P3, we have:
P3 = P1 * (1.00 L / 1.00 L) * (30 + 273.15 K) / (2000 + 273.15 K)
Therefore, to find the answers to these questions, simply substitute the given values into the equations and calculate the pressures accordingly.