A block of aluminum at is quickly submerged in of water initially at inside a…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

0.25\,\text{kg}

block of aluminum at

100\,^{\circ}\text{C}

is quickly submerged in

0.50\,\text{kg}

of water initially at

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

inside a perfectly insulating container. Take the specific heat capacities to be

c_{\text{Al}} = 0.90\,\text{J}\,(\text{g}\,^{\circ}\text{C})

and

c_{\text{water}} = 4.18\,\text{J}\,(\text{g}\,^{\circ}\text{C})

. Assume no phase change occurs and neglect energy exchange with the container walls. (a) Determine the final equilibrium temperature of the aluminum–water mixture. (b) Using the convention

Q>0

for energy entering a system, calculate the value and sign of

Q_{\text{Al}}

for the aluminum block. (c) For the water defined as a separate system, calculate

Q_{\text{water}}

and state whether the water undergoes heating or cooling. (d) Define a larger system consisting of both the aluminum and the water. Determine the net thermal energy transfer

Q_{\text{net}}

for this combined system and discuss how your result is consistent with energy conservation.

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