High School

What is the specific heat capacity of a 5.0 kg object that requires 67,500 J to have its temperature raised by [tex]$30^{\circ} C$[/tex]?

Answer :

To solve this problem, we need to determine the specific heat capacity of the object. The specific heat capacity can be found using the formula:

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

Where:
- [tex]\( c \)[/tex] is the specific heat capacity.
- [tex]\( Q \)[/tex] is the amount of heat energy absorbed or released, in joules (J).
- [tex]\( m \)[/tex] is the mass of the object, in kilograms (kg).
- [tex]\( \Delta T \)[/tex] is the change in temperature, in degrees Celsius ([tex]\(^{\circ}C\)[/tex]).

Given the values:
- [tex]\( Q = 67500 \, \text{J} \)[/tex]
- [tex]\( m = 5.0 \, \text{kg} \)[/tex]
- [tex]\( \Delta T = 30 \, ^{\circ}C \)[/tex]

We can substitute these values into the formula to find the specific heat capacity:

[tex]\[
c = \frac{67500}{5.0 \times 30}
\][/tex]

When you perform the calculation:

1. Multiply the mass [tex]\( m \)[/tex] by the temperature change [tex]\( \Delta T \)[/tex]:
[tex]\[ 5.0 \times 30 = 150 \][/tex]

2. Divide the heat energy [tex]\( Q \)[/tex] by the result from step 1:
[tex]\[ c = \frac{67500}{150} \][/tex]

3. Calculate the result from step 2:
[tex]\[ c = 450.0 \, \text{J/kg}^{\circ}C \][/tex]

Therefore, the specific heat capacity of the object is [tex]\( 450.0 \, \text{J/kg}^{\circ}C \)[/tex].