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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.?
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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.
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The internal energy of an ideal gas is given by U=3.5pV k, where k is ...
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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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