Assume that the kinetic energy of a 1400 kg car moving at 115 km/h (Problem 1.78) is converted entirely into heat. How many calories of heat are released, and what amount of water in liters could be heated from 20.0 °C to 50.0 °C by the car's energy? (One calorie raises the temperature of 1 mL 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 the conversion factor (1000 m/1 km) and dividing by the time conversion factor (3600 s/1 h).
2. Calculate the kinetic energy (KE) of the car using the formula KE = \(\frac{1}{2}mv^2\), where \(m\) is the mass of the car and \(v\) is its velocity in m/s.
3. Convert the kinetic energy from joules to calories, knowing that 1 joule is approximately 0.239005736 calories.
4. Calculate the total amount of heat in calories that would be required to raise the temperature of water from 20.0 °C to 50.0 °C. Use the formula \(Q = mc\Delta T\), where \(m\) is the mass of the water in grams, \(c\) is the specific heat capacity of water (1 cal/g°C), and \(\Delta T\) is the change in temperature.
5. Determine the volume of water in liters that could be heated using the total calories calculated from the kinetic energy, knowing that 1 mL of water has a mass of 1 gram and there are 1000 mL in a liter.

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 is 1400 kg and its speed is converted from km/h to m/s to find the kinetic energy in joules, which will later be converted to calories.

Caloric Conversion

The conversion between joules and calories is essential for this problem. One calorie is defined as the amount of energy needed to raise the temperature of 1 gram of water by 1 °C. Knowing that 1 calorie equals approximately 4.184 joules allows us to convert the kinetic energy calculated into calories to determine how much heat is released.

Specific Heat Capacity

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 1 cal/g°C, meaning that to heat water from 20.0 °C to 50.0 °C, we can use the heat energy calculated from the car's kinetic energy to find out how many grams (or liters, since 1 mL of water has a mass of 1 g) can be heated to that temperature.