Question

The engine of a Ferrari F355 F1 sports car takes in air at 20°C and 1.00 atm and compresses it adiabatically to 0.09
times the original volume. The air may be treated as an ideal diatomic gas.
a) Draw a pV-diagram for this process.
b) Find the final temperature and pressure

Answer 1

Answer on Question #83937 Physics / Molecular Physics | Thermodynamics

The engine of a Ferrari F355 F1 sports car takes in air at $t_1 = 20{}^\circ \mathrm{C}$ and $p_1 = 1.00$ atm and compresses it adiabatically to 0.09 times the original volume. The air may be treated as an ideal diatomic gas $\left(\gamma = \frac{\tau}{5}\right)$ .

a) Draw a pV-diagram for this process.

b) Find the final temperature and pressure.

Solution:

a) The pV-diagram for adiabatic process is as follows

b) Using equations of the adiabatic process,

$$p _ {1} V _ {1} ^ {\gamma} = p _ {2} V _ {2} ^ {\gamma}, \quad T _ {1} V _ {1} ^ {\gamma - 1} = T _ {2} V _ {2} ^ {\gamma - 1}$$

we obtain

$$p _ {2} = p _ {1} \left(\frac {V _ {1}}{V _ {2}}\right) ^ {\gamma} = 1. 0 0 \mathrm {a t m} \left(\frac {1}{0 . 0 9}\right) ^ {\frac {7}{5}} = 2 9. 1 \mathrm {a t m}$$ $$T _ {2} = T _ {1} \left(\frac {V _ {1}}{V _ {2}}\right) ^ {\gamma - 1} = 2 9 3 \mathrm {K} \left(\frac {1}{0 . 0 9}\right) ^ {\frac {7}{5} - 1} = 7 6 8 \mathrm {K}$$

Answer: 29.1 atm, 768 K

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