How Is Work Done by Gas Calculated in a Thermodynamic System?

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In a thermodynamic system with a gas in a cylinder and a frictionless piston, 1400 kcal of heat is added, causing the volume to increase from 12.0 m³ to 17.7 m³. To calculate the work done by the gas, the equation W = PΔV is used, where P is the atmospheric pressure and ΔV is the change in volume. The change in internal energy (ΔU) can be calculated using the equation ΔU = Q - W, where Q is the heat added. The challenge arises from needing to convert kcal to joules and determining the pressure to find the work done. The discussion highlights the importance of understanding the relationship between heat, work, and internal energy in thermodynamic processes.
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Homework Statement


A gas is enclosed in a cylinder fitted with a light frictionless piston and maintained at atmospheric pressure. When 1400 kcal of heat is added to the gas, the volume is observed to increase slowly from 12.0 m3 to 17.7 m3. Calculate the following
(a) work done by the gas ____ J
(b) change in internal energy of the gas ____ J

Homework Equations


(delta)U = Q - W


The Attempt at a Solution


I tried to convert 1400 kcal to J and plug it into the problem, but it appears that I have two unknown variables and I'm not really sure where to go from here.
 
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The work on a isobaric process (since the piston is free to move without friction) is given by the equation W = P.\DeltaV
 
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