How would you calculate the work associated with the compression of a gas from 121.0 L to 80.0 L at a pressure of 13.1 atm?
Assuming this is an ideal gas:
Let's convert liters to cubic meters first so that our units work out.
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To calculate the work associated with the compression of a gas, you can use the formula:
[ W = -P_{\text{ext}} \Delta V ]
Where:
- ( W ) is the work done on the gas (in joules).
- ( P_{\text{ext}} ) is the external pressure (in atmospheres).
- ( \Delta V ) is the change in volume of the gas (in liters).
Given:
- ( P_{\text{ext}} = 13.1 ) atm
- Initial volume, ( V_i = 121.0 ) L
- Final volume, ( V_f = 80.0 ) L
Substitute the values into the formula:
[ \Delta V = V_f - V_i = 80.0 , \text{L} - 121.0 , \text{L} = -41.0 , \text{L} ]
[ W = - (13.1 , \text{atm}) \times (-41.0 , \text{L}) ]
[ W = 537.1 , \text{L} \cdot \text{atm} ]
[ \text{Since } 1 , \text{L} \cdot \text{atm} = 101.3 , \text{J}, ]
[ W = 537.1 \times 101.3 = 54387.23 , \text{J} ]
So, the work associated with the compression of the gas is ( 54387.23 , \text{J} ).
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