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A cylinder with a piston holds 4.00 moles of a monatomic gas. The gas in the cylinder absorbs 975 J of energy due to the higher temperature of the environment. At the same time, the cylinder expands to a larger volume, doing 147 J of work on the environment.(a)What is the change in internal energy of the gas in the cylinder (in J)? J(b)What is the change in temperature of the gas (in K)? K

Question

A cylinder with a piston holds 4.00 moles of a monatomic gas. The gas in the cylinder absorbs 975 J of energy due to the higher temperature of the environment. At the same time, the cylinder expands to a larger volume, doing 147 J of work on the environment.(a)What is the change in internal energy of the gas in the cylinder (in J)? J(b)What is the change in temperature of the gas (in K)? K

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Solution

(a) The change in internal energy (ΔU) of the gas can be calculated using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system (Q) minus the work done by the system (W). In this case, Q = 975 J (the energy absorbed by the gas) and W = 147 J (the work done by the gas on the environment). So, ΔU = Q - W = 975 J - 147 J = 828 J.

(b) The change in temperature (ΔT) of the gas can be calculated using the formula ΔU = nCvΔT, where n is the number of moles of gas, Cv is the molar heat capacity at constant volume for a monatomic gas (which is 3/2 R, where R is the gas constant and equals 8.314 J/(mol·K)), and ΔT is the change in temperature. Rearranging the formula gives ΔT = ΔU / (nCv) = 828 J / (4.00 mol * 3/2 * 8.314 J/(mol·K)) = 828 J / (4.00 mol * 12.471 J/(mol·K)) = 16.6 K.

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