Question

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.

Answer 1

`T = 34.493\,^(\textdegree)C`

Step-by-step explanation:

The equilibrium temperature of the gas-container system is:

`Q_(Cu) = -Q_(g)`

`(0.3\,kg)\cdot\left(386\,(J)/(kg\cdot ^(\textdegree)C) \right)\cdot (T-20\,^(\textdegree)C) = (1.5\,mol)\cdot \left(12.5\,(J)/(mol\cdot ^(\textdegree)C) \right)\cdot (124\,^(\textdegree)C-T)`

`\left(115.8\,(J)/(^(\textdegree)C) \right)\cdot (T-20\,^(\textdegree)C) = \left(18.75\,(J)/(^(\textdegree)C) \right)\cdot (124\,^(\textdegree)C-T)`

`134.55\cdot T = 4641`

`T = 34.493\,^(\textdegree)C`