Two metal samples, X and Z, of the same mass and initially at 25.0 degrees Celsius, are heated so that each metal receives the same amount of thermal energy. Which metal will have the highest final temperature? Specific heat capacity of X = 0.350 J/g⁰C and specific heat of Z = 0.895 J/g⁰C

X = 27.86°C

Y = 26.11°C

Explanation:

Hello,

To solve this question, we'll need to relate heat energy with specific heat capacity

Q = mc∇T

Q = heat energy

M = mass of substance

C = specific heat capacity of substance

∇T = T2 - T1 = change in temperature of the substance.

For X,

Q = mc∇T

Assuming m = 1 g and Q = 1J

T = 25°C

Q = mc(T2 - T1)

1 = 1 × 0.350 × (T2 - 25)

1 = 0.350T2 - 8.75

8.75 + 1 = 0.350T2

Solve for T2

T2 = 9.75 / 0.350

T2 = 27.86°C

For Z

Assuming Q = 1J and M = 1g

Q = mc∇T

Q = mc(T2 - T1)

1 = 1 × 0.895 (T2 - 25)

1 = 0.895T2 - 22.375

22.375 + 1 = 0.895T2

23.375 = 0.895T2

Solve for T2

T2 = 23.375 / 0.895

T2 = 26.11°C

Since both X and Z have equal mass and same energy was passed through them, the final temperature of X = 27.86°C and Z = 26.11°C

As a general observation, whenever comparing two specific heat capacities of different metals, the metal with the greater value of specific heat capacity would have the lower final temperature while the metal with the lower specific heat capacity would have the higher temperature.

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