Question

Recall the general equation for pressure volume work and the equations for the four special cases we have considered; a free expansion, an expansion against constant pressure and a reversible, isothermal expansion of a perfect gas and the adiabatic expansion of a perfect gas. (Even though we say expansions, for all but free expansion processes, the same equations hold for compressions as well.) Give the appropriate equation for calculating work in the following typed problems. These problems came from several different textbooks. Some of these use the term ideal gas instead of perfect gas. Calculate complete answers to problems 3, 4 and 7, and the problem 2.7 found at the end of this document 1. If a balloon filled to a volume of 1.25 L with a perfect gas is placed in a sealed chamber at a constant temperature of 18oC and the pressure in the chamber increased slowly until the balloon is squeezed to 1.00 L how much work is done on the gas in the balloon? 2. A nonideal (non perfect) gas is heated slowly and expands reversibly at a constant pressure of 275 torr from a volume of 385 cm3 to 875 cm3. Find the work in Joules. 3. A balloon 15 m in diameter is inflated with helium at 20oC. How much work is done during inflation against an external pressure of 1 atm. (101325 Pa), from initial volume of zero to its final volume? 4. 1.5 mol of a gas that behaves perfectly was allowed to expand reversibly and isothemrally at 27oC to twice its volume. Calculate w in units of J/mol. 5. A 3.75 mol sample of an ideal gas with CV,m = 3R/2 initially at a temperature Ti = 298 K and pi = 1.00 bar is enclosed in an adiabatic piston and cylinder assembly. The gas is compressed by placing a 725 kg mass on the piston with a diameter of 25.4 cm. Calculate the work done in this process. Assume that the mass of the piston is negligible. 6. The You Tube video found at http://www.youtube.com/watch?v=d4Rz7c0NJSE&feature=related shows a large weather balloon being filled and released from the ground. About 5 minutes into this video the balloon and its payload is free and rising into the atmosphere. The balloon is a bubble of helium gas inside a gas bag much larger than the bubble. You can see this in the wrinkles in the sack and the large amount of fabric hanging below the helium bubble. Atmospheric pressure decreases with elevation as shown below The flexible cloth of the balloon allows the pressure inside and outside of the balloon to remain in equilibrium. Calculate the work done by the expanding gas as the balloon rises from sea level to 5000 m assuming the temperature remains constant. 7. A pellet of Zn of mass 14.5 g is dropped into a flask containing dilute H2SO4 at a pressure of 1.00 bar and 25oC. What is the reaction involved? How much work is done? 8. 2.25 mol of an ideal (perfect) gas at 35.6oC expands isothermally from an initial volume of 26.0 dm3 to a final volume of 40.0 dm3 Calculate the work done A. For an expansion against constant external pressure of 1.00 x 105 Pa B. For a reversible expansion 9.Calculate w for the adiabatic expansion of 1 mole of an ideal (perfect) gas at an initial pressure of 2.25 bar and temperature of 475 K to a final temperature of 322 K. 10. A 1.50 mole sample of an ideal gas initially at 28.5oC expands reversibly and adiabatically from an initial volume of 22.5 dm3 to a final volume of 75.5 dm3. 11. The work done by an engine may depend on its orientation in a gravitational field, because the mass of a piston is relevant when the expansion if vertical. A chemical reaction takes place in a container of cross-sectional area 55.0 cm2; the container has a piston of mass 250 g at one end. As a result of the reaction, the piston is pushed out (a) horizontally, (b) vertically through a distance of 155 cm against an external pressure of 105 kPa. Calculate the work done in each case. 12. A sample of blood plasma occupies 0.550 L at 0oC and 1.03 bar is compressed iso-thermally by 0.57% by being subjected to a constant external pressure of 95.2 bar. Calculate w.

Answer 1

1. To calculate the work done for isothermal expansion or compression, the formula is:

w = nRT ln (V₂/V₁)

w = work done

n = number of moles of gas

T = temperature

V₂ = final volume

V₁ = initial volume

So, for this problem, R = 8.314 J K-1 mol-1

T = 18 oC = 273+18 = 291 K

V1 = 1.25 L

V2 = 1.00 L

So, w = 8.314*291 ln (1.00/1.25)

= -539 J

So, work is done on the system as the work done is negative.

2) To claculate the work done at constant pressure, the formula is:

w = PV

P = constant pressure

V = change in volume

P = 275 torr = 275*133 Pa = 36663 Pa

V = (875-385) cm3 = 490 cm3 = 490*0.001 = 0.490 L

So, work done = 36663*0.490 = 17.964 kJ

3) Intial diameter of balloon = 0 m

Final diameter of balloon = 15 m

radius = 15/2 = 7.5 m

volume of a sphere = (4/3) r³

= (4/3) (3.14) (7.5)³

= 1766.25 m3

= 1766.25*10³ L

V = 1766.25*10³ L

P = 1atm = 101325 Pa

So, work done = PV = 101325*(1766.25*10³) = 1.8*10¹¹ J

4) w = nRT ln (V₂/V₁)

n = number of moles of gas = 1.5 mol

T = temperature = 27 ^oC = 300 K

V₂ = 2V

V₁ = V

So, for this problem, R = 8.314 J K-1 mol-1

So, w = 1.5*8.314*300 ln (2V/V)

= 2593 J/mol

So, work is done by the system as the work done is positive.