A gas contained in a cylinder is filled with a frictionless piston expands against a constant pressure $1$ atmosphere from a volume of $4$ litre to a volume of $14$ litre. In doing so, it absorbs $800 J$ thermal energy from surroundings. Determine $Δ U$ for the process.

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Solution

Given, $q = 800 J$
$Δ V = (14 - 4) = 10$ litre
$w = - P \times Δ V = - 1 \times 10 = - 10 l i t r e - a t m$
But $0.082$ litre-atm $= 1.987 c a l$
So, $w = \frac{10 \times 1.987}{0.082} = - 242.3 c a l$
But $1$ calorie $= 4.184 J$
So, $w = - 242.3 \times 4.184 = - 1013.7 J$
Substituting the values in the equation
$Δ U = q + w = (800 - 1013.7) = - 213.7 J$

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A gas contained in a cylinder is filled with a frictionless piston expands against a constant pressure 1 atmosphere from a volume of 4 litre to a volume of 14 litre. In doing so, it absorbs 800J thermal energy from surroundings. Determine ΔU for the process.

Given, q=800JΔV=(14−4)=10 litrew=−P×ΔV=−1×10=−10litre−atmBut 0.082 litre-atm=1.987calSo, w=10×1.9870.082=−242.3calBut 1 calorie=4.184JSo, w=−242.3×4.184=−1013.7JSubstituting the values in the equationΔU=q+w=(800−1013.7)=−213.7J

A gas contained in a cylinder is filled with a frictionless piston expands against a constant pressure $1$ atmosphere from a volume of $4$ litre to a volume of $14$ litre. In doing so, it absorbs $800 J$ thermal energy from surroundings. Determine $Δ U$ for the process.