In a diesel engine, the piston compresses air at 302 K to a volume that is 0.0628 of the original volume and a pressure that is 48.2 times the original pressure. What is the temperature of the air after the compression?

Can anyone help me work this problem?

Use the combined gas law.

I'm not sure what that is.

Certainly! To solve this problem, we need to use the ideal gas law equation, which states that the product of pressure (P) and volume (V) of an ideal gas is directly proportional to its temperature (T) in Kelvin:

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)

In this specific problem, the initial temperature (T1) is given as 302 K, and the ratio of the final volume (V2) to the original volume (V1) is 0.0628. The ratio of the final pressure (P2) to the original pressure (P1) is 48.2.

Now, let's proceed with finding the temperature of the air after compression.

Step 1: Convert the original and final volumes to the same unit of measurement.
If the original volume is given in liters or any other unit, you need to convert it to cubic meters.

Step 2: Calculate the final volume.
Using the given ratio of volumes:
V2 = V1 * 0.0628

Step 3: Calculate the final pressure.
Using the given ratio of pressures:
P2 = P1 * 48.2

Step 4: Rearrange the ideal gas law equation to solve for temperature:
T2 = (P2 * V2) / (n * R)

Step 5: Substitute the known values and solve for T2:
T2 = (P1 * 48.2 * V1 * 0.0628) / (n * R)

Step 6: Substitute the given values:
T2 = (P1 * 48.2 * V1 * 0.0628) / (n * 8.314)

Note: Since the number of moles and the ideal gas constant are not provided in the problem, we cannot calculate the specific value for temperature. However, you can substitute known values into the equation to solve for temperature with provided values.

Remember to pay attention to units while performing calculations.