Question #8f7d4
1 Answer
Explanation:
QUICK ANSWER
If you take
135 color(red)(cancel(color(black)("g"))) * (T_f - 21)color(red)(cancel(color(black)(""^@"C"))) = 82.5 color(red)(cancel(color(black)("g"))) * (89 - T_f)color(red)(cancel(color(black)(""^@"C")))
This will get you
T_f = (82.5 * 89 + 135 * 21)/(135 + 82.5)
color(darkgreen)(ul(color(black)(T_f = 47))) " " -> rounded to two sig figs
You can thus say that the final temperature of the sample will be
THE DETAILED VERSION
Assuming that no heat is lost to the surroundings, you can say that the heat lost by the warmer sample will be equal to the heat gained by the colder sample.
color(blue)(ul(color(black)(q_"gained" = - q_"lost")))" "color(darkorange)("(*)") The minus sign is used here because heat lost carries a negative sign.
Now, the amount of heat gained/lost depends on the mass of the substance,
color(blue)(ul(color(black)(q = m * c * DeltaT)))
If you take
q_"gained" = "135 g" * c_"water" * (T_f - 21)^@"C"
Similarly, the heat lost by the warmer sample will be
q_"lost" = "82.5 g" * c_"water" * (T_f - 89)^@"C"
Use equation
135 color(red)(cancel(color(black)("g"))) * color(red)(cancel(color(black)(c_"water"))) * (T_f - 21) color(red)(cancel(color(black)(""^@"C"))) = - 82.5 color(red)(cancel(color(black)("g"))) * color(red)(cancel(color(black)(c_"water"))) * (T_f - 89)color(red)(cancel(color(black)(""^@"C")))
This simplifies to
135 * (T_f - 21) = - 82.5 * (T_f - 89)
which is equivalent to
135 * (T_f - 21) = 82.5 * (89 - T_f)
Once again, you will find that the final temperature of the sample will be
The answer must be rounded to two sig figs, the number of sig figs you have for the two temperatures.