To solve this problem, you can use the equation that relates the thermal energy (Q) needed to raise the temperature of a certain mass of a substance by a specific number of degrees Celsius. The equation is:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the thermal energy in joules (J),
- \( m \) is the mass of the substance in kilograms (kg),
- \( c \) is the specific heat capacity in joules per kilogram per degree Celsius \( \left( \frac{J}{kg \cdot °C} \right) \),
- \( \Delta T \) is the change in temperature in degrees Celsius (°C).
Now, let's apply the given values to the formula:
- The mass \( m \) of the substance is 5 kg,
- The specific heat capacity \( c \) is 300 \( \frac{J}{kg \cdot °C} \),
- The temperature change \( \Delta T \) is 10°C.
Plugging in these values, we get:
\[ Q = (5 \, kg) \times (300 \, \frac{J}{kg \cdot °C}) \times (10 \, °C) \]
Multiplying these values together, we find the thermal energy \( Q \):
\[ Q = 5 \times 300 \times 10 \]
\[ Q = 1500 \times 10 \]
\[ Q = 15000 \, J \]
Therefore, the amount of thermal energy needed to raise the temperature by 10°C of 5 kg of a substance with a specific heat capacity of 300 J/(kg °C) is 15,000 joules.
