Answer :
The specific heat capacity is approximately 0.31 J/kg°C when the change in internal energy is 182 J and mass is 19 kg.
To find the specific heat capacity [tex](\(C\))[/tex], we can use the formula:
[tex]\[ \Delta Q = mc\Delta T \][/tex]
Where:
[tex]\(\Delta Q\)[/tex] is the change in internal energy (given as 182 J)
[tex]\(m\)[/tex] is the mass (given as 19 kg)
[tex]\(c\)[/tex] is the specific heat capacity (what we're trying to find)
[tex]\(\Delta T\)[/tex] is the change in temperature (given as 31°C)
We rearrange the formula to solve for [tex]\(c\)[/tex]:
[tex]\[ c = \frac{\Delta Q}{m\Delta T} \][/tex]
Substitute the given values into the formula:
[tex]\[ c = \frac{182 \, \text{J}}{19 \, \text{kg} \times 31 \, \text{\°C}} \][/tex]
[tex]\[ c = \frac{182}{589} \, \text{J/kg\°C} \][/tex]
[tex]\[ c = 0.31 \, \text{J/kg\°C} \][/tex]
So, the specific heat capacity is approximately [tex]\(0.31 \, \text{J/kg\°C}\).[/tex]
