a bus engine can operate at very high temperatures . if one of the cylinders has a volume of 1 litre and is initially at 25°C and atmospheric pressure , what is the temperature when the gas in the cylinder is reduced to a volume of 100cubic centrimeters and pressure of 5000kPa
Assume the number of moles stays the same in the compressed state. (If combustion occurs, this may not quite be true). Then
P*V/T = constant, if T is in degrees K.
(1.013*10^5 Pa)*(1000 cc)/298K = (5.00*10^6 Pa)(100 cc)/T2
Solve for the final temperature T2 in Kelvin. Change to degrees C after that, if they want you to.
T2 = 298*4.94 = 1470 K
To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where:
P = Pressure (in pascals)
V = Volume (in cubic meters)
n = Number of moles of gas
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature (in kelvin)
To convert the given values to SI units:
1 liter = 1000 cubic centimeters
Pressure: 5000 kPa = 5000 * 1000 Pa = 5,000,000 Pa
Volume: 100 cubic centimeters = 0.1 liters = 0.1 * 1000 cubic centimeters = 100 * 10^-6 cubic meters
First, we need to calculate the initial number of moles of gas. Since the pressure and volume are at atmospheric conditions, we can assume the gas behaves ideally. To do this, we will use the ideal gas law rearranged to solve for n:
n = PV / RT
Given that the initial pressure (P) is atmospheric pressure, which is typically around 101,325 Pa, and the initial temperature (T) is 25°C = 25 + 273.15 K, we can substitute these values into the equation:
n = (101325 Pa) * (1 liter) / ((8.314 J/(mol·K)) * (25 + 273.15 K))
Now we have the initial number of moles of gas (n).
To find the final temperature (T), we rearrange the ideal gas law equation to solve for T:
T = PV / (nR)
Plugging in the given values:
P = 5,000,000 Pa
V = 100 * 10^-6 cubic meters
n (calculated earlier)
T = (5,000,000 Pa) * (100 * 10^-6 cubic meters) / ((n moles) * (8.314 J/(mol·K)))
Now you can substitute the calculated value of n into the equation and solve for T.