Why multiply atm by atmospheric pressure in pascals?

[gibson101]

Consider the following two-step process. Heat is allowed to flowout of an ideal gas at constant volume so that its pressure dropsfrom PA = 2.7 atmto 1.4 atm. Then the gas expands at constant pressure, from avolume of 6.8 L to VC = 13.1 L where the temperature reaches its originalvalue. See Fig. 15-27.

In the following work, why is 1.4 atm multiplied by 1.013e5 pascals? And to clarify, PA=2.7 just means pressure A.
Figure 15-27
(a) Calculate the total work done by the gas in the process (in joules).
Work done by gas along the parts BC W2= PdV
= P( Vc-Vb)

= 1.4*1.013*105( 13.1-6.8)*10-3
=893.466J

 

[gneill]

Consider the following two-step process. Heat is allowed to flowout of an ideal gas at constant volume so that its pressure dropsfrom PA = 2.7 atmto 1.4 atm. Then the gas expands at constant pressure, from avolume of 6.8 L to VC = 13.1 L where the temperature reaches its originalvalue. See Fig. 15-27.

In the following work, why is 1.4 atm multiplied by 1.013e5 pascals? And to clarify, PA=2.7 just means pressure A.
Figure 15-27
(a) Calculate the total work done by the gas in the process (in joules).
Work done by gas along the parts BC W2= PdV
= P( Vc-Vb)

= 1.4*1.013*105( 13.1-6.8)*10-3
=893.466J

It's a unit conversion. The equation requires that the pressure be in pascals, and 1 atm = 1.01325 x 10⁵ pascals.

 

[gibson101]

So to get to joules of work, you have to multiply pascals times volume? And why is the answer divided by a thousand (10^-3)?

 

[gneill]

So to get to joules of work, you have to multiply pascals times volume? And why is the answer divided by a thousand (10^-3)?

Because the volume should be in cubic meters, and the values given in liters. How many liters in a cubic meter?

 

[gibson101]

1 liter = .001 m^3. So pascals times cubic meters equals joules? I'm confused.

 

[gneill]

1 liter = .001 m^3. So pascals times cubic meters equals joules? I'm confused.

No need to be confused. Pressure x volume does indeed have the units of energy.