Why multiply atm by atmospheric pressure in pascals?

AI Thread Summary
The discussion centers on the calculation of work done by an ideal gas during a two-step process involving heat flow and expansion. The pressure of the gas, initially at 2.7 atm and dropping to 1.4 atm, is converted to pascals for the calculation, as the formula requires pressure in SI units. The work done is calculated using the formula W = P(Vc - Vb), where the volume must be in cubic meters, necessitating a conversion from liters. The division by 1,000 accounts for this conversion, as 1 liter equals 0.001 cubic meters. Overall, the process illustrates the relationship between pressure, volume, and energy in thermodynamic calculations.
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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
 
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gibson101 said:
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.
 
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)?
 
gibson101 said:
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?
 
1 liter = .001 m^3. So pascals times cubic meters equals joules? I'm confused.
 
gibson101 said:
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.
 

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