To find out how much thermal energy is required to raise the temperature of a substance, you can use the formula:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the thermal energy in joules (J) or kilojoules (kJ)
- \( m \) is the mass of the substance in kilograms (kg)
- \( c \) is the specific heat capacity in J/(kg·°C) or kJ/(kg·°C)
- \( \Delta T \) is the change in temperature in degrees Celsius (°C)
In this case, you want to raise the temperature of water, which has a specific heat capacity \( c = 4.18 \) kJ/(kg·°C), from 10°C to 26°C. The mass of the water is 2 kg.
First, calculate the change in temperature:
\[ \Delta T = T_{final} - T_{initial} = 26°C - 10°C = 16°C \]
Now we can plug the values we have into the formula:
\[ Q = mc\Delta T = 2 \, \text{kg} \times 4.18 \, \text{kJ/(kg·°C)} \times 16°C \]
\[ Q = 2 \times 4.18 \times 16 \]
\[ Q = 8.36 \times 16 \]
\[ Q = 133.76 \, \text{kJ} \]
So it takes 133.76 kJ of thermal energy to raise the temperature of 2 kg of water from 10°C to 26°C.
