Section 7.1: Temperature and Heat
Temperature is a measure of the average kinetic energy of particles in a substance. Heat is the energy transferred between systems due to a temperature difference.
\( Q \) = heat added/removed (J)
\( m \) = mass (kg)
\( c \) = specific heat capacity (J/kg·°C)
\( \Delta T \) = change in temperature (°C)
Heat flows spontaneously from hotter objects to cooler ones until thermal equilibrium is reached.
Example 1: Heating Water
How much energy is required to heat 2 kg of water from 20°C to 80°C? Take \( c = 4180 \text{ J/kg°C} \).
\[
Q = mc\Delta T = 2 \times 4180 \times (80-20) = 501,600 \text{ J}
\]
The energy required is 501.6 kJ.
Example 2: Cooling Metal
A 0.5 kg piece of aluminum cools from 100°C to 25°C. Find the heat lost. Take \( c = 900 \text{ J/kg°C} \).
\[
Q = mc\Delta T = 0.5 \times 900 \times (100-25) = 33,750 \text{ J}
\]
The aluminum loses 33.75 kJ of heat.
Practice Problems
- Calculate the energy needed to raise 3 kg of water from 25°C to 75°C. (c = 4180 J/kg°C)
- A metal block of mass 2 kg at 200°C is placed in 1 kg of water at 25°C. Assuming no heat loss to surroundings, find the final temperature.
- How much heat is released when 500 g of copper cools from 150°C to 50°C? (c = 385 J/kg°C)
- An iron rod of mass 5 kg is heated from 30°C to 100°C. Calculate the heat absorbed. (c = 450 J/kg°C)
- How much energy is required to melt 0.2 kg of ice at 0°C? (Latent heat of fusion Lf = 334,000 J/kg)
- Water at 90°C is poured into 250 g of water at 20°C. Find the final temperature assuming no heat loss.
- A 0.1 kg ice cube melts completely at 0°C. Calculate the heat absorbed. (Lf = 334,000 J/kg)
- Calculate the heat required to raise 0.5 kg of oil from 25°C to 75°C. (c = 2000 J/kg°C)
- A 1 kg aluminum pan absorbs 10,000 J of heat. Find the temperature change. (c = 900 J/kg°C)
- A 2 kg copper block at 80°C is placed in 3 kg of water at 25°C. Find the final equilibrium temperature. (c_cu = 385 J/kg°C, c_water = 4180 J/kg°C)