Specific Heat & Temperature Changes Practice Problems

Thermal regulation of a room involves heating and cooling. If a newly constructed room in a house has a volume of 15400 L and a temperature of 5.0°C, what quantity of heat is required to raise the temperature of the room to the WHO recommended room temperature of 18°C?  Take the specific heat capacity of air to be 1020 J/kg•K and the mass of 1.0L of air to be 1.3 × 10^-3 kg.

Some individuals consider it faster and time-saving to boil water in an electric kettle before transferring it into cookware for subsequent use. If a 2200 W electric kettle is used to heat 1.80 kg of water from 25°C to 90°C, determine the period required to boil the water. Assume water absorbs 100% of the heater's power. 

According to the conservation of energy, energy is not destroyed or created but can be converted to other forms of energy. Suppose 75% of the supplied kinetic energy by a 2.50 kg hammer at a speed of 10.2 m/s when hammering a block is converted into heat energy of the block. Determine the gain in temperature of a 500 g iron block when hammered 8 times. 

A 2.0 kg iron ball is released from a 48.0 m tall building. The ball remains intact upon hitting the ground. If all the ball's mechanical energy is converted into heat energy of the ball, determine the rise in temperature of the ball.

A 3.0 kW electric heater is used to heat a copper pot filled with water which is initially at a temperature of 30°C. It takes 4 minutes for the water to reach the boiling point. If the mass of only the copper pot is 1 kg, Determine the volume of water, in cm³, that was present in the copper pot.

An electric circulation heater is used to heat a liquid solution in a 1.0 cm diameter tube. The heater has a power output of 25 kW and is insulated to prevent heat loss. The solution flows through the tube at a rate of 9.0 L/min. If the initial temperature of the solution is 15°C, what will be the final temperature of the solution after passing through the heater? Assume the electric heater transfers all of its heat energy to the liquid solution, which has a specific heat capacity of 3820 J/kg.K and a density similar to that of water.

A metal rod made of aluminum with a mass of 200 grams is initially at 25°C. Calculate the final temperature of the rod when 1500 J of heat is added. The specific heat capacity of aluminum is 0.897 J/gC°.

A steam pipe contains 150 grams of steam initially at 120°C. Calculate the final temperature of the steam when 2000 J of heat is added. Assume that the pipe is perfectly insulated and does not conduct heat, so all the added heat goes directly into the steam. The specific heat capacity of steam is 2.02 J/gC°.

In a laboratory experiment, iron, silver, and ethyl alcohol are heated, each absorbing the same amount of heat and experiencing a temperature rise of 10.0 °C. Calculate the ratio of their masses. Use the following specific heat variables for the three materials: iron ($4.50\times 10^2$ J/kg·°C), silver ($2.30\times 10^2$ J/ kg·°C), and ethyl alcohol C₂​H₅​OH ($2.40\times 10^3$ J/kg·°C).

A 900-W electric kettle is used to heat 1.0 L of water initially at 20.0°C. The kettle itself is made of 350 g of copper. Assume that no water boils out of kettle and that the kettle is located at sea level.

a) How long does it take to bring the water to a boil inside of the kettle?

b) For how long could the energy that was used to boil the water be used to run a 75-W lightbulb?

Note that the specific heat capacity of copper is 387 J/kg$\cdot$°C; the specific heat capacity of water is 4184 J/kg$\cdot$°C, and the density of water is 1.0 kg/L.

In a challenging refrigeration cycle, the refrigerant is initially at a pressure of 2 atm and a temperature of -10 degree. It is then compressed to 1/8 of its original volume. If the final pressure after compression is 16 atm, estimate the final temperature of the refrigerant, assuming no heat exchange with surroundings.

How much energy does it require to heat a swimming pool that contains 120000 Liters of water from 10°C to 40 °C?

A 0.25-kg steel ball at a high temperature is initially dropped into 2.00 L of water in a 0.50-kg steel container at 25.0°C. Calculate the initial temperature of the steel ball if the final equilibrium temperature is 30.0°C.

[Hint: Specific heat capacity of steel and water is 460 J/kg^.°C and 4186 J/kg^.°C respectively].

A 0.12-kg copper ball is released from a height of 40 meters above the ground. If the ball absorbs 70% of its kinetic energy as thermal energy upon impact, what is the increase in temperature of the ball? Assume that the specific heat capacity for copper is 390 J/kg⋅°C.

A researcher is studying the heat absorption properties of ethanol. They heat a 310-g copper block to 190 °C and then place it into a 98-g stainless steel container holding 260 g of ethanol at an initial temperature of 15 °C. Estimate the specific heat capacity of ethanol if the final temperature is observed to be 41 °C. [Hint: The specific heat capacity of copper and stainless steel are 3.9 × 10² J/kg⋅°C and 5.0 × 10² J/kg⋅°C respectively.]

In a crucial experiment to determine thermal properties, a physics student needs to calculate the total heat capacity for a system consisting of two different materials: copper and lead. The mass of copper used is 5 kg with a specific heat capacity of 390 J/kg K, and lead has a mass of 3 kg with a specific heat of 130 J/kg K. This calculation is a fundamental part of understanding thermal properties and their practical applications. Calculate their combined total heat capacity.

A car engine releases about 2.5×10⁷ J of energy from burning 2.0 kg of gasoline. If a car runs continuously for 6 hours at an average power output of 85 W, how much gasoline does it consume?

A tennis player hits a ball towards a wall such that it approaches at a velocity of 18 m/s and rebounds at 12 m/s. The loss in kinetic energy due to impact heats up the tennis ball. Calculate how much the temperature of the ball increases if the specific heat capacity of tennis ball material is 1500 J/kg·°C.

An electric kettle is used to heat 510 g of water. The kettle can increase the temperature of the water from 25°C to 95°C in 2 minutes or 120 s. Calculate i) the rate at which the energy is transferred to the water. ii) How many grams of water will boil away if the kettle is operated for 3 min rather than for just 120 s and if the power that is transferred from the kettle to the water remains constant? Note that the latent heat of vaporization of water is L = 2260 kJ/kg, and the specific heat capacity of water is c = 4186 J/kg⋅°C.

Simplifying the structure of things can sometimes give us an estimate of quantities. To explore this concept, calculate how much heat must be extracted from a cube of air, the sides of which are of length of 1.0 km, to reduce its temperature by 1.0 K. Assume that the specific heat capacity of air is 720 J/kg⋅°C and its density is 1.2 kg/m³.

An air conditioner is heating an auditorium of dimensions 15 m × 21 m × 6.0 m. The rate of heat provided to the air in the auditorium by the air conditioner is 1.5 × 10⁶ J/h. Initially, the air in the auditorium is at 15°C and 1.0 atm. Calculate the increase in temperature inside the auditorium in one hour. For simplicity, assume that the air is composed of diatomic molecules with a molecular mass of 28.

A 15-g steel ball moving at a velocity of 230 m/s strikes a slender wall and exits the wall at a speed of 150 m/s. Calculate the increase in the steel ball's temperature if the ball absorbs 60% of the heat produced during this process. [Hint: The specific heat capacity of steel is 460 J/kg.°C].

Engineers are testing a new design of a pile driver consisting of a heavy weight of 120 kg. The weight is dropped onto a 25 kg steel pile on the ground. The weight strikes the pile at a speed of 9.5 m/s and comes to a stop. What is the approximate temperature rise of the pile if the weight strikes the pile 6.0 times in rapid succession? Assume that the specific heat capacity of steel is 450 J/kg⋅°C.

A food inspector takes a 35-g sample of potato chips and places it in a small iron container of mass 0.45 kg filled with oxygen. He then places it in 2.5 kg of water in an iron calorimeter cup of mass 0.85 kg at a temperature of 12 °C. Afterward, the oxygen-potato chip mixture in the small container is combusted, and the equilibrium temperature turns out to be 48 °C. If the food inspector does not make any error in his calculations, what would his estimate of the Calories be in 85 g of potato chips? [Hint: The specific heat capacities of iron and water are 0.11 kcal/kg⋅°C and 1.0 kcal/kg⋅°C respectively.]

A 1.5 m in diameter and 35 cm deep glass vessel is filled with ethyl alcohol. Heat is supplied at an average rate of 450 W/m². Find the time required to raise the temperature of the ethyl alcohol from 25°C to 40°C if all the heat is absorbed by the ethyl alcohol. Assume there is no heat loss to surroundings.

While racing, two RC bikes lose control and collide head-on, each traveling at 35 km/h. Following the impact, their kinetic energy is converted into thermal energy. Determine the rise in temperature for each RC bike, considering that their specific heat is similar to that of plastic,  which is approximately 2.1 J/g°C.

A water pump impeller can be considered to stir the water in an isolated system. Calculate heat absorbed by 2.0L of water when its temperature rises from 18°C to 60°C if no net flow of water occurs.

How much heat is lost when an aluminum cube of length 0.12 m cools from 140°C to 20°C?

A chef is heating a 4.8 kg cooking oil to prepare a large batch of fried food. If the oil starts at 22.0°C and is heated to 76.0°C, calculate the specific heat of the oil, given that 158 kJ of heat energy is absorbed during this process.

You have a 100-gram block of a special alloy kept in a storage facility at -20°C. The alloy has a specific heat capacity of 2.1 J/gC°. To test the material's heating response, 1000 J of heat is applied to the alloy. What will the final temperature of the alloy be after adding the 1000 J of heat?