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In this lesson, we will learn how to describe the exchange of energy between objects that heat each other and observe how their temperatures change as a result.

Q1:

Two perfectly insulated gas canisters contain air with a specific heat capacity of 1 0 0 5 / ⋅ J k g C ∘ and a density of 1.35 kg/m. One cylinder contains 25 L of air at a temperature of 3 5 ∘ C and the other contains 15 L of air at a temperature of 4 5 ∘ C . The canisters are connected and the gas in both is allowed to come to an equilibrium temperature. Find the equilibrium temperature to three significant figures.

Q2:

Some hot water that has a mass of 750 g and a temperature of 7 5 ∘ C is poured over 1 500 g of an unknown substance that has a temperature of 1 5 ∘ C . The temperatures of the water and the substance are both monitored. At an instant 𝑡 , the water temperature is 5 5 ∘ C and the substance temperature is 2 5 ∘ C . Find the specific heat capacity of the substance. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the water’s specific heat capacity. Assume that the water does not heat its surroundings.

Q3:

A 2.5 L volume of water at a temperature of 8 8 ∘ C is added to a perfectly insulated container that holds a 45 kg block of lead. After the water and the lead have equalized each other’s net heating, the temperature of both substances is 8 5 ∘ C . Find the initial temperature of the lead block. Use a value of 4 , 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water and a value of 1 3 0 / ⋅ J k g C ∘ for the specific heat capacity of lead. Answer to three significant figures.

Q4:

A brick has a mass of 4.5 kg, a temperature of 9 5 ∘ C , and a specific heat capacity of 8 4 0 / ⋅ J k g C ∘ . The brick is dropped into a perfectly insulated water tank containing 15 kg of water at a temperature of 9 . 5 ∘ C . At an instant 𝑡 after the brick has been dropped into the water, the temperature of the water is 1 1 . 5 ∘ C . Find the temperature of the brick at 𝑡 . Answer to the nearest degree. Use a value of 4 , 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water.

Q5:

The graph shows the changes in temperature with time of different objects. Each object has a different temperature after eight minutes of cooling, and all the objects’ initial temperatures are different from each other. Which of the following statements most correctly expresses what is shown by the curves drawn in the graph?

Q6:

The graph shows the changes in temperature with time of different objects. Each object has a different temperature after eight minutes of cooling, but all the objects’ temperatures are initially the same. At any given time, one object is cooling at a greater rate than any of the other objects at that same time. Find the temperature of this object after eight minutes. Answer to one significant figure.

Q7:

What temperature would all the objects eventually have, given unlimited cooling time?

At any given time, one object is cooling at a greater rate than any of the other objects at that same time. What is the initial temperature of this object?

Q8:

An open-topped cylinder contains water and a metal cube, as shown in the diagram. The water and the cube are both at the same temperature. The metal cube heats the water in the cylinder at a rate of 36 W and the water heats the cube at a rate of 12 W. The air directly above the cylinder is heated at a rate of 14 W. At what rate is the cylinder heated?

Q9:

The objects A, B, and C in the diagram have the temperatures 𝑇 , 𝑇 , and 𝑇 respectively. The temperature of object A is the same as the temperature of object C. The temperature of object C is the same as the temperature of object B. How does 𝑇 compare to 𝑇 ?

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