Physics

Problem

0.40\,\text{kg}

aluminum block at

120\,^{\circ}\!\text{C}

is dropped into

0.80\,\text{kg}

of water initially at

20\,^{\circ}\!\text{C}

inside a perfectly insulated cup. After a short time the block and water reach

40\,^{\circ}\!\text{C}

. An identical

0.40\,\text{kg}

aluminum block, also at

120\,^{\circ}\!\text{C}

, is then added to the same cup. Which statement best describes the final equilibrium temperature

T_f

of the system? (Assume no energy is lost to the surroundings.) a)

T_f

will be exactly

40\,^{\circ}\!\text{C}

because the original block and water are already in equilibrium. b)

T_f

will be between

40\,^{\circ}\!\text{C}

and

120\,^{\circ}\!\text{C}

, but closer to

40\,^{\circ}\!\text{C}

than to

120\,^{\circ}\!\text{C}

. c)

T_f

will be exactly

80\,^{\circ}\!\text{C}

because that is the average of

40\,^{\circ}\!\text{C}

and

120\,^{\circ}\!\text{C}

. d)

T_f

will be between

40\,^{\circ}\!\text{C}

and

120\,^{\circ}\!\text{C}

, but closer to

120\,^{\circ}\!\text{C}

than to

40\,^{\circ}\!\text{C}