Final answer:
To find the final temperature of a monoatomic ideal gas after adiabatic compression to one-eighth its volume from an initial temperature of 17°C, we apply the formula for adiabatic processes. Considering that γ for a monoatomic gas is 5/3, we find that the final temperature is approximately 887°C.
Step-by-step explanation:
The question you've asked relates to the adiabatic compression of an ideal gas, which is a concept in thermodynamics, a branch of physics. Specifically, you're interested in finding the final temperature of a monoatomic ideal gas after it is compressed adiabatically to one-eighth of its original volume, beginning from an initial temperature of 17°C.
For an adiabatic process in a monoatomic ideal gas, we can use the formula relating the initial and final states of the gas: T1 * V1γ-1 = T2 * V2γ-1, where γ (gamma) is the heat capacity ratio (Cp/Cv), which is 5/3 for a monoatomic ideal gas. Given that the volume changes to one-eighth (V2 = V1/8), we can rearrange the formula to solve for the final temperature (T2).
Starting from the initial temperature (T1) of 17°C, which is 290K (since we need to convert to Kelvin for these calculations), we can insert the values into the equation and solve for T2. The calculation indicates the final temperature will be significantly higher than the initial temperature due to the work done on the gas during compression. We find that T2 is approximately 887°C after compression.