Question

Mercury has one of the lowest specific heats. This fact added to its liquid state at most atmospheric temperatures makes it effective for use in thermometers. If 257 J of energy are added to 0.450 kg of mercury, the mercury’s temperature will increase by 4.09 K. What is the specific heat of mercury?

Answer 1

To find the specific heat of mercury, we can use the formula for calculating the heat absorbed or released by a substance, which is given by:

\[ Q = mc\Delta T \]

where:
- \( Q \) is the heat energy (in joules),
- \( m \) is the mass of the substance (in kilograms),
- \( c \) is the specific heat capacity (in J/(kg·K)),
- \( \Delta T \) is the change in temperature (in Kelvin).

From the problem, we know:
- \( Q = 257 \, \text{J} \)
- \( m = 0.450 \, \text{kg} \)
- \( \Delta T = 4.09 \, \text{K} \)

We need to find the specific heat \( c \). Rearranging the formula gives:

\[ c = \frac{Q}{m \Delta T} \]

Now, substituting the given values into the equation:

\[
c = \frac{257 \, \text{J}}{0.450 \, \text{kg} \times 4.09 \, \text{K}}
\]

Calculating the denominator:

\[
0.450 \, \text{kg} \times 4.09 \, \text{K} = 1.8435 \, \text{kg·K}
\]

Now, substituting this back into our equation for \( c \):

\[
c = \frac{257 \, \text{J}}{1.8435 \, \text{kg·K}} \approx 139.5 \, \text{J/(kg·K)}
\]

Thus, the specific heat of mercury is approximately:

\[
\boxed{139.5 \, \text{J/(kg·K)}}
\]