Final answer:
The pressure and temperature at the end of adiabatic compression in an ideal OTTO cycle with a compression ratio of 6:1 are 1244.5 kPa and 599.96 K, respectively.
Step-by-step explanation:
The adiabatic compression of an ideal gas in an Otto cycle refers to the process of compressing a gas without any heat transfer to or from the surroundings. In this process, both the temperature and pressure of the gas increase. To find the pressure and temperature at the end of adiabatic compression, we can use the adiabatic compression formula:
P₂ / P₁ = (V₁ / V₂)^(γ-1)
Where P₁ and V₁ are the initial pressure and volume, P₂ and V₂ are the final pressure and volume, and γ is the heat capacity ratio.
Given that the compression ratio is 6:1, the initial conditions are 101.3 kPa and 20°C, and we need to find the pressure and temperature at the end of adiabatic compression:
P₁ = 101.3 kPa
P₂ = ?
V₁ = 1
V₂ = 1/6
T₁ = 20°C + 273.15 = 293.15 K
T₂ = ?
Now, we can substitute these values into the adiabatic compression formula and solve for P₂:
P₂ / 101.3 = (1/6)^((5/3)-1)
P₂ = 1244.5 kPa (rounded to one decimal place)
Next, we can use the ideal gas law to find T₂:
P₁V₁ / T₁ = P₂V₂ / T₂
(101.3)(1) / 293.15 = (1244.5)(1/6) / T₂
T₂ = 599.96 K (rounded to two decimal places)