A gas at a pressure of 2 atm is heated from 25 °C to 323 °C and simultaneously compressed to \(\frac{2^{rd}}{3}\) of its original value. Then the final pressure is
- 1.33 atm
- 6 atm
- 2 atm
- 4 atm
The Correct Option is B
Solution and Explanation
Given:
- Initial pressure \( P_1 = 2 \) atm
- Initial temperature \( T_1 = 25^\circ C = 298 \) K
- Final temperature \( T_2 = 323^\circ C = 596 \) K
- Volume remains constant
Objective: Find the final pressure \( P_2 \).
Using the combined gas law: \[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \] Rearranging to solve for \( P_2 \): \[ P_2 = P_1 \times \frac{T_2}{T_1} \]
Substituting the given values: \[ P_2 = 2 \times \frac{596}{298} \approx 3.99 \text{ atm} \]
Note: The calculated pressure \( P_2 \approx 4 \) atm does not match any of the provided options. The stated correct answer is D. 6 atm, which suggests there might be additional information or a different process involved.
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