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In this lesson, we will learn how to relate an object's net temperature to the change to its net heating, its mass, and its specific heat capacity.

Q1:

A 0.250 kg block of a pure material is heated from 2 0 . 0 ∘ C to 6 5 . 0 ∘ C by the addition of 4.35 kJ of energy.

Calculate the specific heat capacity of the material.

Q2:

The same heat transfer into identical masses of different substances produces different temperature changes.

Calculate the final temperature when 1.00 kcal of heat transfers into 1.00 kg of water, originally at 2 0 . 0 ∘ C . The specific heat capacity of water is 1 . 0 0 0 / ⋅ k c a l k g C ∘ .

Calculate the final temperature when 1.00 kcal of heat transfers into 1.00 kg of concrete, originally at 2 0 . 0 ∘ C . The specific heat capacity of concrete is 0 . 2 0 0 / ⋅ k c a l k g C ∘ .

Calculate the final temperature when 1.00 kcal of heat transfers into 1.00 kg of steel, originally at 2 0 . 0 ∘ C . The specific heat capacity of steel is 0 . 1 0 8 / ⋅ k c a l k g C ∘ .

Calculate the final temperature when 1.00 kcal of heat transfers into 1.00 kg of mercury, originally at 2 0 . 0 ∘ C . The specific heat capacity of mercury is 0 . 0 3 3 0 / ⋅ k c a l k g C ∘ .

Q3:

In a study of healthy young men, doing 20 push-ups in 1 minute required an amount of energy per kg that for a 70.0-kg man corresponds to 8.06 calories (kcal). The average specific heat capacity of the human body is 0 . 8 3 0 / ⋅ k c a l k g C ∘ . How much would a healthy, young, 70.0-kg man’s temperature rise if he did not lose any heat while doing 20 push-ups in 1 minute?

Q4:

Two solid spheres, Sphere 𝐴 and Sphere 𝐵 , made of the same material are at temperatures of 0 . 0 ∘ C and 1 0 0 ∘ C respectively. The spheres are placed in thermal contact in an ideal calorimeter and they reach an equilibrium temperature of 2 0 ∘ C . What is the ratio of the diameter of Sphere 𝐴 to the diameter of Sphere 𝐵 ?

Q5:

The specific heat capacity of sodium is 1 2 3 0 / ⋅ J k g C ∘ , and the molar mass of sodium is 23.0 g/mol.

Estimate the specific heat capacity of sodium from the Law of Dulong and Petit.

What percent error results from estimating the specific heat capacity of sodium using the Law of Dulong and Petit, comparing the estimated value to the known value?

Q6:

Rubbing hands together warms them by converting work into heat. A woman rubs her hands back and forth for a total of 35 rubs, where the hands move a distance of 9.0 cm across each other with each rub, against an average frictional force of 31 N. Determine the temperature increase of the warmed parts of her hands, which have a mass of 0.080 kg and a specific heat capacity of 3 5 0 0 / ⋅ J k g C ∘ . Assume no heat loss from the hands during the rubbing process.

Q7:

On a hot day, the temperature of an 8 0 0 0 0 -L swimming pool increases by 1 . 5 0 ∘ C . What is the net heat transfer during this heating? Ignore any complications, such as loss of water by evaporation, and take the specific heat capacity of water to be 4 1 8 6 / ⋅ J k g C ∘ .

Q8:

A nuclear reactor core has a mass of 2 . 3 0 × 1 0 kg. Even when shut down after a period of normal use, the reactor heats its surroundings at the rate of 126 MW by the radioactive decay of fission products. The reactor core has an average specific heat capacity of 3 3 4 9 / ⋅ J k g C ∘ . Under normal circumstances, a cooling system prevents heat generated by an inactive core from raising the core’s temperature, but if the cooling system fails then the core’s temperature can rapidly rise.

What is the rate of temperature increase of the inactive reactor core without cooling? Assume that the lack of cooling means that negligible heating of the core’s surroundings occurs.

How much time would be taken for the inactive reactor core to increase its temperature by 2 0 5 0 ∘ C , assuming that the lack of cooling means that negligible heating of the core’s surroundings occurs?

Q9:

A baby bottle with a mass of 84 g is sterilized by increasing its temperature from 5 . 0 ∘ C to 1 0 0 . 0 ∘ C . Determine how much the bottle must be heated. Use a value of 0 . 8 4 / ⋅ J g C ∘ for the specific heat capacity of glass.

Q10:

The specific heat capacity of an unknown material can be calculated using the empirical formula 𝑐 = 𝛼 + 𝛽 𝑇 + 𝛿 𝑇 − 2 , where 𝛼 = 3 6 7 / ⋅ J k g C ∘ , 𝛽 = 0 . 4 / ⋅ J k g C ∘ − 2 , and 𝛿 = 7 . 8 5 × 1 0 ⋅ / 5 ∘ J C k g . How much heating is needed to raise the temperature of 1.00 kg of mass of the unknown material from 1 0 ∘ C to 3 5 0 ∘ C ?

Q11:

A woman with a mass of 66.0 kg does some vigorous exercise, after which she has a body temperature of 3 9 . 0 ∘ C . Determine the rate at which she must cool her body to reduce its temperature to 3 7 . 0 ∘ C in 3 . 0 0 × 1 0 3 s if it continues to be internally heated at a rate of 110 W. Use a value of 4 1 8 0 / ⋅ J k g C ∘ for the specific heat capacity of the woman’s body.

Q12:

You leave a pastry in the refrigerator on a plate and ask your roommate to take it out before you get home so you can eat it at room temperature, the way you like it. Instead, your roommate plays video games for hours. When you return, you notice that the pastry is still cold, but the game console has become hot. Annoyed, and knowing that the pastry will not be good if it is microwaved, you warm up the pastry by unplugging the console and putting it in a clean trash bag (which acts as a perfect calorimeter) with the pastry on the plate. After a while, you find that the equilibrium temperature is a nice, warm 3 8 . 3 ∘ C . You know that the game console has a mass of 2.1 kg. Approximate it as having a uniform initial temperature of 4 5 ∘ C . The pastry has a mass of 0.16 kg and a specific heat of 3 . 0 / ⋅ k J k g C ∘ and is at a uniform initial temperature of 4 . 0 ∘ C . The plate is at the same temperature and has a mass of 0.24 kg and a specific heat of 0 . 9 0 / ⋅ J k g C ∘ . What is the specific heat of the console?

Q13:

A calorimeter holds 6.59 kg of water at a temperature of 1 9 . 5 ∘ C . A piece of steel of mass 0.50 kg and at a temperature of 1 8 3 ∘ C is put into the water. Determine the equilibrium temperature of the water and steel. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water and 4 9 0 / ⋅ J k g C ∘ for the specific heat capacity of steel. Assume that condensation and evaporation have negligible effect.

Q14:

Some water and some glass are heated by the same amount, increasing their temperatures by the same amount. Determine the ratio of the mass of glass to water. Use a value of 8 4 0 / ⋅ J k g C ∘ for the specific heat capacity of the glass and 4 1 8 6 / ⋅ J k g C ∘ for the specific heat capacity of the water.

Q15:

A piece of metal of mass 0.0500 kg at a temperature of 446 K is dropped into a water tank that contains 0.426 kg of water initially at a temperature of 296 K. Find the equilibrium temperature of the metal and water. Use a value of 5 7 4 / ⋅ J k g C ∘ for the specific heat capacity of the metal and use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water.

Q16:

X-rays form ionizing radiation that is dangerous to living tissue and undetectable to the human eye. Suppose that a student researcher working in an X-ray diffraction laboratory is accidentally exposed to a fatal dose of radiation. Calculate the temperature increase of the unit mass of the researcher under the following conditions: the energy of X-ray photons is 233 keV and the researcher absorbs 6 . 0 0 × 1 0 photons per each kilogram of body weight during the exposure. Assume that the specific heat of the student’s body is 0.800 kcal/kg⋅K.

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