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"A 2.00 mole sample of N^2 gas at 0 ∘C is heated to 190 ∘C at constant pressure (1.00 atm). a) Determine the change in internal energy. b)Determine the work the gas does. c)Determine the heat added to it."
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Answer

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Step 1

First, we need to find the initial and final temperatures in Kelvin. Initial temperature, T^1 (in Kelvin) = 0 ∘C + 273.15 = 273.15 K Final temperature, T^2 (in Kelvin) = 190 ∘C + 273.15 = 463.15 K

Step 2

The formula for the internal energy of an ideal gas is given by U = (f/ 2)nRT, where f is the number of degrees of freedom, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. For diatomic gases like N^2, f = 5. The change in internal energy, ΔU, is given by: Given that f = 5, n = 2.00 moles, and R = 8.314 J/(mol·K), we can calculate ΔU:

Final Answer

a) The change in internal energy, ΔU, is 24,520 J. b) The work done by the gas, W, is 24,520 J. c) The heat added to the gas, Q, is 49,040 J.

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