Questions: What is the specific heat (J / g · °C) of a metal object whose temperature increases by 3.0°C when 17.5 g of metal was heated with 38.5 J? Only enter the correct number, not units!

What is the specific heat (J / g · °C) of a metal object whose temperature increases by 3.0°C when 17.5 g of metal was heated with 38.5 J? Only enter the correct number, not units!
Transcript text: Question 41 3 pts What is the specific heat $\left(\mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$ of a metal object whose temperature increases by $3.0^{\circ} \mathrm{C}$ when 17.5 g of metal was heated with 38.5 J ? Only enter the correct number, not units! $\square$ Next Quiz saved at 6:34am Submit Quiz
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Solution

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Solution Steps

Step 1: Identify the given values

We are given:

  • Mass of the metal, \( m = 17.5 \) g
  • Heat added, \( Q = 38.5 \) J
  • Temperature change, \( \Delta T = 3.0 \)°C
Step 2: Use the specific heat formula

The formula for specific heat \( c \) is: \[ Q = mc\Delta T \]

Step 3: Solve for specific heat \( c \)

Rearrange the formula to solve for \( c \): \[ c = \frac{Q}{m \Delta T} \]

Step 4: Substitute the given values into the formula

\[ c = \frac{38.5 \, \text{J}}{17.5 \, \text{g} \times 3.0 \, ^\circ \text{C}} \]

Step 5: Calculate the specific heat

\[ c = \frac{38.5}{52.5} \] \[ c \approx 0.7333 \]

Final Answer

\(\boxed{0.7333}\)

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