Physics Exam > Physics Questions > 5000J of heat are added to two moles an ideal...
Start Learning for Free
5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)
Correct answer is '400'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
5000J of heat are added to two moles an ideal monoatomic gas, initiall...
ΔU = ΔQ – ΔW = 5000 - 7500
ΔU = –2500 J
⇒ ΔT = –100 K
⇒ T = 500 - 100 = 400 K
The correct answer is: 400
ΔU = –2500 J
⇒ ΔT = –100 K
⇒ T = 500 - 100 = 400 K
The correct answer is: 400
Most Upvoted Answer
5000J of heat are added to two moles an ideal monoatomic gas, initiall...
Given:
- Heat added to the gas (Q) = 5000 J
- Work done by the gas (W) = 7500 J
- Initial temperature of the gas (T₁) = 500 K
- Number of moles of the gas (n) = 2
Key Formulas:
- The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system minus the work done by the system:
ΔU = Q - W
- For an ideal monoatomic gas, the change in internal energy is given by:
ΔU = (3/2) nR ΔT
where R is the gas constant and ΔT is the change in temperature.
- The work done by the gas is given by:
W = -PΔV
where P is the pressure and ΔV is the change in volume.
- For an ideal gas, the change in volume is related to the change in temperature by:
ΔV = nR ΔT/P
Solution:
We can start by using the first law of thermodynamics to find the change in internal energy:
ΔU = Q - W
ΔU = 5000 J - 7500 J
ΔU = -2500 J
Since the gas is monoatomic, we can use the formula for the change in internal energy for an ideal monoatomic gas:
ΔU = (3/2) nR ΔT
-2500 J = (3/2) (2 mol) (8.314 J/(mol·K)) ΔT
-2500 J = 24.942 J/K ΔT
Simplifying the equation:
ΔT = -100.18 K
The negative sign indicates that the temperature has decreased. Therefore, the final temperature of the gas is:
T₂ = T₁ + ΔT
T₂ = 500 K - 100.18 K
T₂ ≈ 400 K
Therefore, the final temperature of the gas is approximately 400 K.
- Heat added to the gas (Q) = 5000 J
- Work done by the gas (W) = 7500 J
- Initial temperature of the gas (T₁) = 500 K
- Number of moles of the gas (n) = 2
Key Formulas:
- The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system minus the work done by the system:
ΔU = Q - W
- For an ideal monoatomic gas, the change in internal energy is given by:
ΔU = (3/2) nR ΔT
where R is the gas constant and ΔT is the change in temperature.
- The work done by the gas is given by:
W = -PΔV
where P is the pressure and ΔV is the change in volume.
- For an ideal gas, the change in volume is related to the change in temperature by:
ΔV = nR ΔT/P
Solution:
We can start by using the first law of thermodynamics to find the change in internal energy:
ΔU = Q - W
ΔU = 5000 J - 7500 J
ΔU = -2500 J
Since the gas is monoatomic, we can use the formula for the change in internal energy for an ideal monoatomic gas:
ΔU = (3/2) nR ΔT
-2500 J = (3/2) (2 mol) (8.314 J/(mol·K)) ΔT
-2500 J = 24.942 J/K ΔT
Simplifying the equation:
ΔT = -100.18 K
The negative sign indicates that the temperature has decreased. Therefore, the final temperature of the gas is:
T₂ = T₁ + ΔT
T₂ = 500 K - 100.18 K
T₂ ≈ 400 K
Therefore, the final temperature of the gas is approximately 400 K.
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer?
Question Description
5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer?.
5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer?.
Solutions for 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer?, a detailed solution for 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? has been provided alongside types of 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup