Consider a container insulated from the environment and divided into two section

Question

Consider a container insulated from the environment 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. 2. 0g of helium at an initial temperature of 310 K 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 monatomic and oxygen is diatomic. ) Express your answer using two significant figures. How much heat energy is transferred? Express your answer using two significant figures.

Explanation / Answer

(A) moles of helium = 2g / 4g/mol = 0.5 mol

moles of oxygen = 7.6g / 32g/mol = 0.2375 mol

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

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

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

or 4796 = 11.172 * final temp

Final temp = 430 K

(B) final energy of helium = 3/2 * 0.5 * 8.314 * 430 = 2677

energy transferred = 2677 - 1933 = 740 Joules (two sig figs)

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