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CBSE
Chemistry
Grade 11
Thermodynamics
Last updated date: 07th Dec 2023 • Total views: 359.1k • Views today: 3.59k
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Calculate the pressure-volume work done by the system when the gas
expands from 1-litre to 2-litre against a constant external pressure of 10
atmosphere. Express the answer in calorie and joule.
Answer
Verified
359.1k+ views
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Hint: Pressure -Volume work done occurs when the volume of the gas or system changes. Work
done by a system is the energy transferred from it to its surroundings. Express that work in
joules and calories, -Pexternal ×△
V
.
Complete step by step answer:
If the gas is heated, the gas molecules are energized. The increase in average kinetic energy of
the gas molecules can be observed by measuring how the temperature of the gas particles
increased. The gas molecules collide with the piston more frequently, by the fast movement of
the gas particles. These frequent collisions transfer energy to the piston and allow it to move
against an external pressure thus, increasing the net volume of the gas.
The work done by the gas is specifically the expansion and compression of the gas. Work done
by gases is sometimes called pressure-volume or PV work.
To calculate how much work is done (or has done to it) by the gas against a constant external
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pressure, we have to use an equation:
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WORK= (w) = -Pexternal ×△
V
where external pressure is denoted by Pexternal . The external
pressure opposes the pressure of the gas in the system. ∆V is a change in the volume of the
gas, which is calculated as Vfinal
− Vin
itial
.
Sign convention of work :
When a system does work on the surroundings, negative work is said to have occurred.
When the gas does work, the volume of the gas particles decreases (△
V
<0).The work done is
positive.
When the gas does work, the volume of the gas particles increases (△
V
>0).The work done is
negative.
Units conversion:
Work has its units in JOULES.
Pressure-volume work has its unit in L-atm which is to be converted to Joules using the
conversion factor 101.325J/1L-atm
To convert joules to calories the conversion factor is 0.239cal/1J.
Calculate the pressure-volume work done by the gas:
Given: Pexternal = 10 atmospheres Vinitial = 1 litre Vfinal = 2 litres
Use the formula, to calculate the work done by the gas:
WORK= (w) = -Pexternal ×△
V
Substitute the values as Vfinal
− Vin
itial
The net formula is
= -Pexternal ×(Vfinal
− Vin
itial
)
Substitute the values of Pexternal ,Vinitial , Vfinal as 10 atmospheres, 1 litre and 2 litres.
The work done is
= - (10 atm)×(2 litres – 1 litre)
= - (10 atm)×(1 litre)
= - (10 litre-atm)
Convert
litre atm
to joules
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factor:
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1 L-atm has 101.325J, so -10 L-atm has (-10)×(101.325J) is equal to (-1013.25 Joules. )
To convert joules into calories multiply the joule by 0.239 factor, (0.239) ×(-1013.25) is equal to
- 242.16 Calories.
The answer of the question is -1013.25 Joules and -242.16 calories.
Note:
(i) Take care of the sign convention while solving the numerical of the work done. As the sign
convention by the gas and on the gas is different.
(ii) Do not forget to convert to use conversion factor for the required units as mentioned in the
question.
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