How would you calculate the work associated with the compression of a gas from 121.0 L to 80.0 L at a pressure of 13.1 atm?

Answer 1

#W_"on gas"~~1.75xx10^5" J"#

Assuming this is an ideal gas:

#W_"env"=-int_(v_i)^(v_f)" P dV"#
#=>W_"env"=-PDeltaV=P(V_"f"-V_"i")#

Let's convert liters to cubic meters first so that our units work out.

#=>V_"i"=0.212" m"^3#
#=>V_"f"=0.08" m"^3#
We also know that #P=13.1" atm"#, which is #1327358 " N"//"m"^2#.
#=>W_"env"=-(1327358 " N"//"m"^2*(0.08" m"^3-0.212" m"^3))#
#=>=-(1327358 " N"//"m"^2*-0.132" m"^3)#
#=>~~1.75xx10^5" Nm"#
#=>~~color(blue)(1.75xx10^5" J")#
#:.# The work done on the gas by the environment to compress the gas is #~~1.75xx10^5" J"#
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Answer 2

To calculate the work associated with the compression of a gas, you can use the formula:

[ W = -P_{\text{ext}} \Delta V ]

Where:

  • ( W ) is the work done on the gas (in joules).
  • ( P_{\text{ext}} ) is the external pressure (in atmospheres).
  • ( \Delta V ) is the change in volume of the gas (in liters).

Given:

  • ( P_{\text{ext}} = 13.1 ) atm
  • Initial volume, ( V_i = 121.0 ) L
  • Final volume, ( V_f = 80.0 ) L

Substitute the values into the formula:

[ \Delta V = V_f - V_i = 80.0 , \text{L} - 121.0 , \text{L} = -41.0 , \text{L} ]

[ W = - (13.1 , \text{atm}) \times (-41.0 , \text{L}) ]

[ W = 537.1 , \text{L} \cdot \text{atm} ]

[ \text{Since } 1 , \text{L} \cdot \text{atm} = 101.3 , \text{J}, ]

[ W = 537.1 \times 101.3 = 54387.23 , \text{J} ]

So, the work associated with the compression of the gas is ( 54387.23 , \text{J} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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