iclicker question 2 (3 mins)
a system fitted with a piston expands when it absorbs 52.3 j of heat from the surroundings. the piston is working against a pressure of 0.851 atm. the final volume is 65.0 l. what was the initial volume of the system if the internal energy of the system decreased by 103.5 j?
a. 58.3 l
b. 71.6 l
c. 118 l
d. 63.2 l
e. 61.4 l

Question

Accepted Answer

# Explanation:
## Step1: Use the first law of thermodynamics
The first law of thermodynamics is $\Delta U=q + w$. Given $\Delta U=- 103.5\space J$ (since internal energy decreased) and $q = 52.3\space J$. First, find the work $w$.
$$
\begin{align*}
w&=\Delta U - q\
w&=-103.5\space J-52.3\space J\
w&=-155.8\space J
\end{align*}
$$
## Step2: Convert work unit and use the formula for work in terms of pressure - volume
The formula for work at constant pressure is $w=-P\Delta V=-P(V_{final}-V_{initial})$. We know $P = 0.851\space atm$. Convert work from joules to liter - atm. Since $1\space L\cdot atm=101.325\space J$, then $w=\frac{- 155.8\space J}{101.325\space J/L\cdot atm}\approx - 1.54\space L\cdot atm$
$$
\begin{align*}
-1.54\space L\cdot atm&=-0.851\space atm\times(65.0\space L - V_{initial})\
\frac{-1.54\space L\cdot atm}{- 0.851\space atm}&=65.0\space L - V_{initial}\
1.81\space L&=65.0\space L - V_{initial}\
V_{initial}&=65.0\space L-1.81\space L\
V_{initial}&=63.2\space L
\end{align*}
$$

# Answer:
D. 63.2 L

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QUESTION IMAGE

Question

Explanation:

Step1: Use the first law of thermodynamics

Step2: Convert work unit and use the formula for work in terms of pressure - volume

Answer: