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A sealed copper container with a mass of 0.3 kg is filled with 1.5 mole of helium gas. Initially, the helium gas is at a temperature of 124 oC and the copper container is at 20 oC. The helium-copper system is thermally isolated. Note that the specific heat of copper is 386 J/(kgK) and the molar specific heat of helium is 12.5 J/(molK). Find the equilibrium temperature of the system.

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Answer:

[tex]T = 34.493\,^{\textdegree}C[/tex]

Explanation:

The equilibrium temperature of the gas-container system is:

[tex]Q_{Cu} = -Q_{g}[/tex]

[tex](0.3\,kg)\cdot\left(386\,\frac{J}{kg\cdot ^{\textdegree}C} \right)\cdot (T-20\,^{\textdegree}C) = (1.5\,mol)\cdot \left(12.5\,\frac{J}{mol\cdot ^{\textdegree}C} \right)\cdot (124\,^{\textdegree}C-T)[/tex]

[tex]\left(115.8\,\frac{J}{^{\textdegree}C} \right)\cdot (T-20\,^{\textdegree}C) = \left(18.75\,\frac{J}{^{\textdegree}C} \right)\cdot (124\,^{\textdegree}C-T)[/tex]

[tex]134.55\cdot T = 4641[/tex]

[tex]T = 34.493\,^{\textdegree}C[/tex]

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