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The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?
answer -1.38
please explain.?
answer -1.38
please explain.?
Most Upvoted Answer
The internal energy of an ideal gas is given by U=3.5pV k, where k is ...
Solution:
Given, U = 3.5pV k and PV^1.3 = constant
We can use the formula for work done by the gas during expansion, which is given by:
W = ∫PdV
Since PV^1.3 = constant, we can write:
P = k/V^1.3
Substituting this value of P in the above formula, we get:
W = ∫k/V^1.3 dV
Integrating both sides, we get:
W = (k/0.3) [V^0.3]0.25^0.86
W = 5.31 kJ (approx.)
Now, we can use the first law of thermodynamics, which states that:
∆U = Q - W
where Q is the heat added to the system and W is the work done by the system.
Since this is an ideal gas, there is no heat added to the system, so Q = 0.
Therefore, ∆U = -W = -5.31 kJ
Converting kJ to J, we get:
∆U = -5.31 × 10^3 J
Rounding off to two decimal places, we get:
∆U = -1.38 J (approx.)
Therefore, the change in internal energy of the gas is -1.38 J.
Given, U = 3.5pV k and PV^1.3 = constant
We can use the formula for work done by the gas during expansion, which is given by:
W = ∫PdV
Since PV^1.3 = constant, we can write:
P = k/V^1.3
Substituting this value of P in the above formula, we get:
W = ∫k/V^1.3 dV
Integrating both sides, we get:
W = (k/0.3) [V^0.3]0.25^0.86
W = 5.31 kJ (approx.)
Now, we can use the first law of thermodynamics, which states that:
∆U = Q - W
where Q is the heat added to the system and W is the work done by the system.
Since this is an ideal gas, there is no heat added to the system, so Q = 0.
Therefore, ∆U = -W = -5.31 kJ
Converting kJ to J, we get:
∆U = -5.31 × 10^3 J
Rounding off to two decimal places, we get:
∆U = -1.38 J (approx.)
Therefore, the change in internal energy of the gas is -1.38 J.
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The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?answer -1.38please explain.?
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The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?answer -1.38please explain.? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?answer -1.38please explain.? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?answer -1.38please explain.?.
The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?answer -1.38please explain.? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?answer -1.38please explain.? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The internal energy of an ideal gas is given by U=3.5pV k, where k is constant. Gas expands from an initial volume of 0.25m3 to 0.86m3. If initial pressure is 5 Nm-2 then find change in internal energy in joules. [Given PV^1.3= const]?answer -1.38please explain.?.
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