Answer :
The final temperature of the system, when two objects with different masses, specific heat capacities, and initial temperatures exchange heat, is approximately 221.5 Kelvin.
To find the final temperature of the system when two objects exchange heat, we can use the principle of conservation of energy. The total energy exchanged between the objects is equal to the sum of their individual energies. The formula for this is:
m1 * c1 * (T - T1) + m2 * c2 * (T - T2) = 0
where:
m1 and m2 are the masses of objects 1 and 2, respectively,
c1 and c2 are the specific heat capacities of objects 1 and 2, respectively,
T is the final temperature of the system, and
T1 and T2 are the starting temperatures of objects 1 and 2, respectively.
Given:
m1 = 14.7 kg
c1 = 1081 J/kg
T1 = 141 K (starting temperature of object 1)
m2 = 14 kg
c2 = 734 J/kg
T2 = 348 K (starting temperature of object 2)
Now, we need to solve for T:
14.7 * 1081 * (T - 141) + 14 * 734 * (T - 348) = 0
Simplify the equation:
15907.7 * (T - 141) + 10276 * (T - 348) = 0
Now, distribute and combine terms:
15907.7T - 2241688.7 + 10276T - 3562848 = 0
Combine like terms:
15907.7T + 10276T = 2241688.7 + 3562848
26183.7T= 5804536.7
Now, solve for T:
T = 5804536.7 / 26183.7
T ≈ 221.5 K
The final temperature of the system is approximately 221.5 Kelvin, rounded to one decimal place.
Learn more about conservation of energy here: https://brainly.com/question/12050604
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