Chapter 18: Problem 9
A large cylindrical tank contains 0.750 m\(^3\) of nitrogen gas at 27\(^\circ\)C and 7.50 \(\times\) 10\({^3}\)Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.410 m\(^3\) and the temperature is increased to 157\(^\circ\)C?
Short Answer
Step by step solution
Understand the Ideal Gas Law
Convert Temperatures to Kelvin
Use the Pressure-Volume-Temperature Relation
Solve for the Final Pressure, P_2
Final Calculation
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Pressure-Volume-Temperature Relation
Temperature Conversion to Kelvin
- \( T(\text{K}) = T(\text{°C}) + 273.15 \)
- \( T_1 = 27 + 273.15 = 300.15\, \text{K} \)
- \( T_2 = 157 + 273.15 = 430.15\, \text{K} \)
Gas Pressure Calculation
- Initial pressure \( P_1 = 7.50 \times 10^3 \text{ Pa} \)
- Initial volume \( V_1 = 0.750 \text{ m}^3 \)
- Initial temperature \( T_1 = 300.15 \text{ K} \)
- Final volume \( V_2 = 0.410 \text{ m}^3 \)
- Final temperature \( T_2 = 430.15 \text{ K} \)