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------------------------------------------------ If the change in internal energy is 84 J, the mass is 28 kg, and the temperature change is [tex]$37^{\circ} C$[/tex], what is the specific heat capacity?

Give your answer to 2 decimal places if needed.

To find the specific heat capacity, we can use the formula:

[tex]\[ c = \frac{\Delta E}{m \times \Delta T} \][/tex]

where:
- [tex]$ c $[/tex] is the specific heat capacity,
- [tex]$\Delta E$[/tex] is the change in internal energy,
- [tex]$ m $[/tex] is the mass,
- [tex]$\Delta T$[/tex] is the temperature change.

Let's plug in the values given in the problem:
- [tex]$\Delta E = 84 \, \text{Joules}$[/tex],
- [tex]$ m = 28 \, \text{kg}$[/tex],
- [tex]$\Delta T = 37 \, ^{\circ}\text{C}$[/tex].

Now substitute the values into the formula:

[tex]\[ c = \frac{84}{28 \times 37} \][/tex]

Calculate the denominator:

[tex]\[ 28 \times 37 = 1036 \][/tex]

Now divide the change in internal energy by the product of mass and temperature change:

[tex]\[ c = \frac{84}{1036} \approx 0.08108108108108109 \][/tex]

Next, round the result to two decimal places:

[tex]\[ c \approx 0.08 \][/tex]

Therefore, the specific heat capacity is approximately [tex]$ 0.08 \, \text{J/kg} \cdot ^{\circ}\text{C} $[/tex].