Question

When we double the compression ratio of an ideal Otto cycle, what happens to the maximum gas temperature and pressure when the state of the air at the beginning of the compression and the amount of heat addition remain the same? Use constant specific heats at room temperature.

Short answer

Answer: To determine the effect on the maximum gas temperature and pressure when the compression ratio of an ideal Otto cycle is doubled, we must first calculate the initial maximum temperature and pressure using the given air state and compression ratio. Once the initial maximum temperature and pressure are found, we must calculate the new maximum temperature and pressure after doubling the compression ratio, considering constant specific heat at room temperature. Comparing the initial and new values, we can understand how the maximum gas temperature and pressure change when the compression ratio is doubled, with the heat addition and air state remaining the same.

Step-by-step solution

Recall the equations for an ideal Otto Cycle

We will need the following equations for an ideal Otto cycle: 1. Efficiency equation: η = 1 - 1/(r^(γ-1)), where r is the compression ratio and γ is the specific heat ratio. 2. Maximum temperature equation: T_max = T1 * (r^(γ - 1)), where T1 is the initial air temperature.

Determine the initial maximum temperature and pressure

Using the given information about the air at the beginning of the compression, we can calculate the initial maximum temperature and pressure using the equations from Step 1.

Calculate the new compression ratio after it is doubled

We are given that the compression ratio is to be doubled. Calculate the new compression ratio by multiplying the initial compression ratio by 2.

Calculate the new maximum temperature and pressure using the new compression ratio

Using the new compression ratio calculated in step 3, we can calculate the new maximum temperature and pressure using the efficiency equation (η) and the maximum temperature equation (T_max) from step 1 considering constant specific heat at room temperature.

Compare the initial and new maximum temperature and pressure

Here, we need to compare the initial and new maximum temperature and pressure calculated in Steps 2 and 4 to determine what happens to the maximum gas temperature and pressure when the compression ratio is doubled while keeping the state of the air at the beginning of the compression and the amount of heat addition the same.