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A gas is compressed from a volume of \mathrm{2.0 \mathrm{~L}} to \mathrm{1.0 \mathrm{~L}} at a constant pressure of \mathrm{2.0 \mathrm{~atm}}. During the compression, the gas releases \mathrm{100 \mathrm{~J}} of heat to the surroundings. Calculate the work done by the gas.

Option: 1

-600 J


Option: 2

350 J


Option: 3

-400 J


Option: 4

202 J


Answers (1)

best_answer

The first law of thermodynamics states that:

                                  \mathrm{ \Delta U=q+w }

where \mathrm{\Delta U} is the change in internal energy of the system, q is the heat added to or removed from the system, and w is the work done by or on the system.Since the pressure is constant, we can use the following equation to calculate the work done by or on the gas:

                                   \mathrm{ w=-P \Delta V }

where P is the pressure and \mathrm{\Delta V} is the change in volume.Substituting the values given, we get:

                             \mathrm{ w=-(2.0 \mathrm{~atm})(1.0 \mathrm{~L}-2.0 \mathrm{~L})=2.0 \mathrm{~L} \text { atm } }

Since \mathrm{1 \mathrm{~L} \, \, atm =101.3 \mathrm{~J}}, we can convert this to joules:

                    \mathrm{ w=(2.0 \mathrm{~L} \mathrm{~atm})(101.3 \mathrm{~J} / \mathrm{L} \mathrm{atm})=202.6 \mathrm{~J} }

Therefore, the work done by the gas is 202.6 J. so, correct option is (D)

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