Final answer:
The compression ratio for an air-standard Diesel cycle can be calculated using the isentropic relationship between the initial and final pressures and temperatures, assuming adiabatic compression for an ideal gas, and potentially considering variable specific heats.
Step-by-step explanation:
The correct answer is that we need to determine the compression ratio for an air-standard Diesel cycle given the initial and final conditions. To calculate the compression ratio r, we use the relationship between the temperatures and pressures at the start and end of the compression process, under the assumption of adiabatic compression for an ideal gas. As the specific heats are variable, we would typically use the variable specific heat capacities and integrate accordingly, but for an ideal gas, we can also use the isentropic relationships. The isentropic relationship between the initial and final pressures and temperatures of an adiabatic process for an ideal gas is given by:
P1 * V1^gamma = P2 * V2^gamma and T1 * V1^(gamma - 1) = T2 * V2^(gamma - 1),
where gamma is the ratio of specific heats (Cp/Cv). As specific heat ratios for air vary depending on temperature and pressure, they should be looked up from a standard table if we are considering variable specific heats. However, for simplicity and lack of those exact values in this example, we could use a standard gamma value for air of 1.4, which holds true at 'normal' conditions. Hence, we could approximate:
r = (V1/V2) = (P2/P1)^(1/gamma) = (T2/T1)^(1/(gamma - 1)),
and by substituting the provided values of pressures and temperatures, we can calculate the approximate compression ratio.