If a process requires 250 joules of work to be done in order to increase the volume of a cylinder of gas from 90 liters to 125 liters at constant pressure, what is the gas pressure during the expansion?
A. 7 × 103 pascals
B. 3 × 104 pascals
C. 2 × 104 pascals
D. 4 × 105 pascals
E. 2 × 103 pascals
To solve this problem, we can use the relationship between work, pressure, and volume in a gas system.
The work done on or by a gas system can be calculated using the formula:
Work = Pressure * Change in Volume
In this case, the change in volume is 125 liters – 90 liters = 35 liters.
We are given that the work done is 250 joules. Now, we need to convert the units to match the formula.
Since 1 liter is equal to 0.001 cubic meters, we can convert the change in volume to cubic meters:
Change in Volume = 35 liters * 0.001 m^3/liter = 0.035 m^3
Now, we need to convert the work from joules to pascals. Recall that 1 Pascal is equal to 1 joule per cubic meter:
Work = 250 joules
Work = 250 joules / 0.035 m^3 = 7143 pascals
Therefore, the gas pressure during the expansion is 7143 pascals.
But we need to match this answer with the options provided. Let's convert 7143 pascals to the closest option:
A. 7 × 103 pascals = 7,000 pascals
B. 3 × 104 pascals = 30,000 pascals
C. 2 × 104 pascals = 20,000 pascals
D. 4 × 105 pascals = 400,000 pascals
E. 2 × 103 pascals = 2,000 pascals
Out of the given options, the closest value to 7143 pascals is 7 × 103 pascals (Option A).
Therefore, the gas pressure during the expansion is approximately 7 × 103 pascals.