First law of thermodynamics: A cylinder contains 23 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.43 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol · K and the ideal gas constant is R = 8.314 J/mol ∙ K. The heat absorbed by the gas is closest to

Question

Quizplus · Accepted Answer

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, the gas is compressed at constant pressure, so the work done by the gas is equal to the change in volume times the pressure. The heat added to the gas is equal to the change in internal energy plus the work done by the gas. The change in internal energy is equal to the number of moles of gas times the molar heat capacity at constant volume times the change in temperature. The change in temperature is equal to the final temperature minus the initial temperature.Plugging in the given values, we get:```Q = U + WQ = nCv(Tf - Ti) + P(Vf - Vi)Q = (23 mol)(24.0 J/mol · K)(300 K - 273 K) + (1 atm)(0.43 Vf - Vf)Q = -130 kJ```Therefore, the heat absorbed by the gas is closest to -130 kJ.

First Law of Thermodynamics: a Cylinder Contains 23 Moles of an Ideal