Topic: Thermodynamics
A sample of gas ($\gamma=1.5$) is taken through an adiabatic process in which the volume is compressed from $1600~cm^{3}$ to $400~cm^{3}$. If initial pressure is 150 kPa, then how much will be the final pressure in the process?
- A. 1200 kPa
- B. 1000 kPa
- C. 1100 kPa
- D. 1400 kPa
Answer: A. 1200 kPa
Explanation: For an adiabatic process, the governing equation is $P_{1}V_{1}^{\gamma} = P_{2}V_{2}^{\gamma}$. Rearranging to solve for the final pressure gives $P_{2} = P_{1}(\frac{V_{1}}{V_{2}})^{\gamma}$. Substituting the given values: $P_{2} = 150 \times (\frac{1600}{400})^{1.5} = 150 \times 4^{1.5}$. Since $4^{1.5} = 8$, the final pressure is $P_{2} = 150 \times 8 = 1200\text{ kPa}$.