A GAS EXPANDS IN VOLUME FROM 26.7 ML TO 89.3 ML AT CONSTANTTEMPERATURE. CALCULATE THE WORK DONE (IN JOULES) IF THE GASEXPANDS (A) AGAINST A VACUUM,(B) AGAINST A CONSTANT PRESSUREOF 1.5 ATM, AND (C) AGAINST A CONSTANT PRESSURE OF 2.8 ATM.
A.
Expansion work (or PV work) is
work = -p(v final-v initial)
If p is zero, the PV work must be zero since any number x zero is zero.
B. Substitute the numbers into -p(v final - v initial). p is 1.5 for B and 2.8 for C.
Delta V is 89.3 - 26.7 = ? mL and change that to L.
Work has units of L*atm. Change to joules by L*atm x 101.325 J/atm = ? J
To calculate the work done by the gas in each scenario, we need to use the formula for work done by a gas during expansion or compression:
Work = Pressure * Change in volume
Before we calculate the work done, we need to convert the given volumes from milliliters to liters, as the standard unit of volume used with pressure is liters.
Given: Initial volume (Vi) = 26.7 mL = 26.7 mL * (1 L / 1000 mL) = 0.0267 L
Final volume (Vf) = 89.3 mL = 89.3 mL * (1 L / 1000 mL) = 0.0893 L
Now, let's calculate the work done in each scenario:
A) Against a vacuum:
As the gas expands against a vacuum, no external pressure is acting on the gas. Therefore, the work done in this scenario is zero (Work = 0 J).
B) Against a constant pressure of 1.5 atm:
Using the formula for work done, we have:
Work = Pressure * Change in volume
Given: Pressure = 1.5 atm
Change in volume = Vf - Vi = 0.0893 L - 0.0267 L = 0.0626 L
Work = 1.5 atm * 0.0626 L = 0.0939 atm * L
To convert the unit from atm * L to Joules (J), we can use the conversion factor:
1 atm * L = 101.325 J
So, Work = 0.0939 atm * L * 101.325 J / 1 atm * L = 9.518 J
Therefore, the work done against a constant pressure of 1.5 atm is 9.518 Joules.
C) Against a constant pressure of 2.8 atm:
Using the same formula for work done, we have:
Work = Pressure * Change in volume
Given: Pressure = 2.8 atm
Change in volume = Vf - Vi = 0.0893 L - 0.0267 L = 0.0626 L
Work = 2.8 atm * 0.0626 L = 0.1748 atm * L
Converting the unit from atm * L to Joules (J) using the conversion factor:
1 atm * L = 101.325 J
Work = 0.1748 atm * L * 101.325 J / 1 atm * L = 17.716 J
Therefore, the work done against a constant pressure of 2.8 atm is 17.716 Joules.