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An ideal monoatomic gas at 27oC is compressed adiabatically to 8/27 times of its original volume. The increase in temperature of the gas is
- a)400oC
- b)375o C
- c)350o C
- d)300o C
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
An ideal monoatomic gas at 27oC is compressed adiabatically to 8/27 ti...
Given:
Initial temperature, T1 = 27 oC
Initial volume, V1 = V
Final volume, V2 = V/3
No heat exchange between the system and the surroundings (adiabatic process)
To find:
Final temperature, T2
Formula used:
PVγ = constant, where γ is the specific heat ratio.
γ = Cp/Cv for monoatomic gas is 5/3.
Adiabatic process: P1V1γ = P2V2γ
Solution:
Using the formula PVγ = constant
P1V1γ = P2V2γ
P1V1^γ = P2(V1/3)^γ
P1/P2 = (V1/V2)γ = (3/1)5/3
P2/P1 = (1/3)5/3
Using the formula P1V1/T1 = P2V2/T2
(P1/P2) = (T1/T2)(V2/V1)
(1/3)5/3 = (T1/T2)(1/3)
T2 = T1/(1/33/5) = 27/(1/33/5)
T2 = 27 x 125
T2 = 3375 K
The increase in temperature = T2 - T1 = 3375 - 27 = 3348 K
The increase in temperature = 3348 - 273 = 307 oC
Therefore, the final temperature of the gas after adiabatic compression is 3375 K or 375 oC.
Initial temperature, T1 = 27 oC
Initial volume, V1 = V
Final volume, V2 = V/3
No heat exchange between the system and the surroundings (adiabatic process)
To find:
Final temperature, T2
Formula used:
PVγ = constant, where γ is the specific heat ratio.
γ = Cp/Cv for monoatomic gas is 5/3.
Adiabatic process: P1V1γ = P2V2γ
Solution:
Using the formula PVγ = constant
P1V1γ = P2V2γ
P1V1^γ = P2(V1/3)^γ
P1/P2 = (V1/V2)γ = (3/1)5/3
P2/P1 = (1/3)5/3
Using the formula P1V1/T1 = P2V2/T2
(P1/P2) = (T1/T2)(V2/V1)
(1/3)5/3 = (T1/T2)(1/3)
T2 = T1/(1/33/5) = 27/(1/33/5)
T2 = 27 x 125
T2 = 3375 K
The increase in temperature = T2 - T1 = 3375 - 27 = 3348 K
The increase in temperature = 3348 - 273 = 307 oC
Therefore, the final temperature of the gas after adiabatic compression is 3375 K or 375 oC.
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Community Answer
An ideal monoatomic gas at 27oC is compressed adiabatically to 8/27 ti...
Use formula TV^gaama-1=constant
T1V1^gaama-1=T2V2^gaama-1
substitute the given terms and you will find T2
now subtract 27c from T2
that is T2-27 in centigrade
T1V1^gaama-1=T2V2^gaama-1
substitute the given terms and you will find T2
now subtract 27c from T2
that is T2-27 in centigrade
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An ideal monoatomic gas at 27oC is compressed adiabatically to 8/27 times of its original volume. The increase in temperature of the gas isa)400oCb)375o Cc)350o Cd)300o CCorrect answer is option 'B'. Can you explain this answer?
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