Air in a diesel engine cylinder is quickly compressed from an initial temperature of 21.1°C, an initial pressure of 1.00 atm, and an initial volume of 670 cm^3 to a final volume of 44.5 cm^3.

a) Assuming the air to be an ideal diatomic gas, find the final temperature (in K).

b) Assuming the air to be an ideal diatomic gas, find the final pressure

The specific heat ratio for a diatomic gas is 7/5.

Assume an adiabatic process with
P*V^1.4 = constant

b) P2/P1 = (V1/V2)^1.4

a) Once you have P2, use the ideal gas law for T2.

You do the rest.

To solve this problem, we need to use the ideal gas law, which states:

PV = nRT

where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

Since the air is assumed to be an ideal diatomic gas, we also need to consider the fact that it consists of two atoms per molecule. Hence, we'll use the molar mass of the air and divide it by two to get the molar mass of one diatomic molecule.

a) Finding the final temperature:
1. Convert the initial temperature from Celsius to Kelvin by adding 273.15:
T_initial = 21.1 + 273.15 = 294.25 K

2. Rearrange the ideal gas law to solve for T:
T_final = (P_final * V_final) / (n * R)

3. Determine the number of moles:
n = (m / M) / 2
Where m is the mass of air and M is the molar mass.
Since the mass is not given in the problem, we cannot continue calculating the final temperature without additional information.

b) Finding the final pressure:
1. Rearrange the ideal gas law to solve for P:
P_final = (n * R * T_final) / V_final

Again, we need to know the number of moles (n) to continue calculating the final pressure. Without this information, we cannot proceed with the calculation.