Calculate Work Done on 1 Mole of Ideal Gas at Constant Pressure | 298K

In summary, the question asks for the calculation of work done to compress 1 mole of ideal gas from 1atm to 0.5atm at 298K, assuming a constant external pressure of 1atm. The equation for work done is -Integral pdV. By substituting the given values, the work done is calculated to be 2270J. There is a discrepancy in the question where one statement mentions a change in pressure and the other mentions a constant pressure, so it is unclear whether the highlighted quantities should be volumes instead.
  • #1
quietrain
655
2

Homework Statement



calculate work done to compress 1mole of ideal gas from 1atm to 0.5atm at 298K
where it is subjected to constant external pressure of 1atm

Homework Equations


Won = -Integral pdV = -(1atm)(Vf-Vi) = -p(RT/pf - RT/pi) = 2270J

where i have assumed T does not change, is it correct to assume so?

because i read that T changes proportionally with V, if so, how do i find what is my (Vf-Vi)

thanks!
 
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  • #2
quietrain said:

Homework Statement



calculate work done to compress 1mole of ideal gas from 1atm to 0.5atm at 298K
where it is subjected to constant external pressure of 1atm

Homework Equations


Won = -Integral pdV = -(1atm)(Vf-Vi) = -p(RT/pf - RT/pi) = 2270J

where i have assumed T does not change, is it correct to assume so?

because i read that T changes proportionally with V, if so, how do i find what is my (Vf-Vi)

thanks!
Are you sure that you have the question copied correctly. In particular, could you check that the two highlighted quantities should not be volumes?
 
  • #3
yes that's what the question wrote

thats why i found it strange.

shouldn't it be vol, so that its just P(vf-vi)?
 
  • #4
quietrain said:
yes that's what the question wrote

thats why i found it strange.

shouldn't it be vol, so that its just P(vf-vi)?
That would be my guess. There are two conflicting statements. The first specifies a change in pressure, whilst the second asserts a constant pressure.
 
  • #5
ok thank you!
 

1. What is PV work done?

PV work done refers to the work done by a system as a result of a change in its volume and pressure. It is a measure of the energy transferred to or from the system due to changes in its internal state.

2. How is PV work calculated?

PV work is calculated by multiplying the change in the system's volume by the change in its pressure. In equation form, it can be written as W = PΔV, where W represents work, P represents pressure, and ΔV represents change in volume.

3. What are the units of PV work?

The units of PV work are joules (J) in the SI system. In some cases, it may also be expressed in other units such as kilojoules (kJ) or calories (cal).

4. What is the significance of PV work in thermodynamics?

PV work is a key concept in thermodynamics, as it represents the energy transferred in a system due to changes in its volume and pressure. It is used to analyze and understand processes such as compression, expansion, and heat transfer in various systems.

5. Can PV work be negative?

Yes, PV work can be negative. This occurs when the system does work on its surroundings, rather than the other way around. This may happen, for example, when a gas expands against an external pressure. In this case, the work done by the gas is negative, as it is losing energy to the surroundings.

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