Assume that the kinetic energy of a 1400-kg car moving at 115 km/h (Problem 9.46) could be converted entirely into heat. What amount of water could be heated from 20 °C to 50 °C by the car's energy? 4.184 J are required to heat 1 g of water by 1 °C.

Verified step by step guidance

1. Convert the speed of the car from km/h to m/s by multiplying by \(\frac{1000 \text{ m}}{1 \text{ km}}\) and dividing by \(\frac{3600 \text{ s}}{1 \text{ h}}\).
2. Calculate the kinetic energy (KE) of the car using the formula \(KE = \frac{1}{2} m v^2\), where \(m\) is the mass of the car and \(v\) is its velocity in m/s.
3. Determine the total amount of heat energy required to raise the temperature of water from 20 °C to 50 °C using the formula \(Q = mc\Delta T\), where \(m\) is the mass of the water in grams, \(c\) is the specific heat capacity of water (4.184 J/g°C), and \(\Delta T\) is the change in temperature.
4. Set the kinetic energy calculated in step 2 equal to the heat energy calculated in step 3 to find the mass of water that can be heated, solving for \(m\).
5. Convert the mass of water from grams to kilograms if necessary by dividing by 1000.

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v², where m is mass and v is velocity. In this scenario, the car's mass and speed are used to determine the total kinetic energy, which is then converted into heat energy.

Heat Transfer and Specific Heat Capacity

Heat transfer refers to the movement of thermal energy from one object to another, while specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is 4.184 J/g°C, indicating how much energy is needed to heat water, which is crucial for calculating how much water can be heated by the car's energy.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In this problem, the kinetic energy of the car is entirely converted into thermal energy, which is then used to heat water, illustrating the transformation of energy types while adhering to conservation laws.