Consider a container insulated from the enviroment and divided into two sections

Question

Consider a container insulated from the enviroment and divided into two sections by a very thin, stiff membrane, with n1 moles of a monatomic gas on one side and n2 moles of a diatomic gas on the other. The monatomic gas has initial temperature T1i. The diatomic gas has initial temperature T2i.

Part A) 2.0 g of helium at an initial temperature of 310K interacts thermally with 7.6g of oxygen at an initial temperature of 580K. What is the final temperature? (Hint: The total thermal energy is conserved, so the initial thermal energy must equal the final thermal energy. However, helium is monoatomic and oxygen is diatomic.)

Part B) How much heat energy is transferred?

Explanation / Answer

moles of helium = 2 grams / 4 grams per mol = 0.5 mol

moles of oxygen = 7.6 / 32 grams per mol = 0.2375 mole

initial energy of helium = 3/2 nRT = 3/2 * 0.5 * 8.314 * 310 = 1933 Joules

initial energy of oxygen = 5/2 nRT = 5/2 * 0.2375 * 8.314 * 580 = 2863 Joules

total energy = 1933 + 2863 = 4796 = 3/2 * 0.5 * 8.314 * final temp + 5/2 * 0.2375 * 8.314 * final temp

final temp = 429 Kelvin

final energy of helium = 3/2 * 0.5 * 8.314 * 429 = 2677 Joules

energy transferred = 2677 - 1933 = 744 Joules

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