A Lab Assistant Drops a 400 $100.0 ^ { \circ } \mathrm { C }$

A lab assistant drops a 400.0-g piece of metal at $100.0 ^ { \circ } \mathrm { C }$ into a 100.0-g aluminum cup containing 500.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ In a few minutes, she measures the final temperature of the system to be $40.0 ^ { \circ } \mathrm { C }$ What is the specific heat of the 400.0-g piece of metal, assuming that no significant heat is exchanged with the surroundings? The specific heat of this aluminum is $900.0 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A) $3300 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $3800 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $2270 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $4280 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
E) $1900 \mathrm {~J} / \mathrm { kq } \cdot \mathrm { K }$

Correct Answer:

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