Question

a piece of silver with a mass 386 g has a heat capacity of 91.5 j/°c. what is the specific heat of silver? be sure your answer has the correct number of significant digits.

Explanation:

Step1: Recall the formula for specific heat

The formula that relates heat capacity (\(C\)), mass (\(m\)), and specific heat (\(c\)) is \(C = m\times c\). We need to solve for \(c\), so we can rearrange the formula to \(c=\frac{C}{m}\).

Step2: Identify the given values

We are given that the mass \(m = 386\space g\) and the heat capacity \(C=91.5\space\frac{J}{^\circ C}\).

Step3: Substitute the values into the formula

Substitute \(C = 91.5\space\frac{J}{^\circ C}\) and \(m = 386\space g\) into the formula \(c=\frac{C}{m}\). So we have \(c=\frac{91.5\space\frac{J}{^\circ C}}{386\space g}\).

Step4: Perform the division

Calculate \(\frac{91.5}{386}\). Let's do the division: \(91.5\div386\approx0.237\space\frac{J}{g\cdot^\circ C}\) (we consider the significant digits: 91.5 has three significant digits and 386 has three significant digits, so the result should have three significant digits).

Answer:

\(0.237\)