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Multiple Choice
An unknown gas expands in a container increasing the volume from 4.3 L to 8.2 L at a constant pressure of 931 mmHg. Calculate the internal energy of the system if the system absorbs 2.3 kJ of energy.
A
2.3 kJ
B
1.8 kJ
C
1.2 kJ
D
2.8 kJ
Verified step by step guidance
1
Identify the given values: initial volume (V1) = 4.3 L, final volume (V2) = 8.2 L, constant pressure (P) = 931 mmHg, and energy absorbed (q) = 2.3 kJ.
Convert the pressure from mmHg to atm for consistency in units, using the conversion factor: 1 atm = 760 mmHg.
Calculate the work done by the system using the formula: \( w = -P \Delta V \), where \( \Delta V = V2 - V1 \). Ensure the pressure is in atm and the volume change is in liters.
Use the first law of thermodynamics, which states \( \Delta U = q + w \), where \( \Delta U \) is the change in internal energy, \( q \) is the heat absorbed, and \( w \) is the work done by the system.
Substitute the values of \( q \) and \( w \) into the equation to find \( \Delta U \). Remember to convert the work from L·atm to kJ using the conversion factor: 1 L·atm = 0.1013 kJ.