Question

A system fitted with a piston expands when it absorbs 53.1 ) of heat from the surroundings. The piston is working against a pressure of 0.677 atm. The final volume is 63.2 L. What was the initial volume of the system if the internal energy of the system decreased by 108.3 J?
a. 65.6 L
b. 64.0 L
c. 70.8 L
d. 60.8 L
e. 54.4L

Answer 1

Answer:

d. 60.8 L

Explanation:

Step 1: Given data

• Heat absorbed (Q): 53.1 J

• External pressure (P): 0.677 atm

• Final volume (V2): 63.2 L

• Change in the internal energy (ΔU): -108.3 J

Step 2: Calculate the work (W) done by the system

We will use the following expression.

ΔU = Q + W

W = ΔU - Q

W = -108.3 J - 53.1 J = -161.4 J

Step 3: Convert W to atm.L

We will use the conversion factor 1 atm.L = 101.325 J.

-161.4 J ×  1 atm.L/101.325 J = -1.593 atm.L

Step 4: Calculate the initial volume

First, we will use the following expression.

W = - P × ΔV

ΔV = - W / P

ΔV = - 1.593 atm.L / 0.677 atm = 2.35 L

The initial volume is:

V2 = V1 + ΔV

V1 = V2 - ΔV

V1 = 63.2 L - 2.35 L = 60.8 L