**Title: Heat Radiation from Spheres in a Vacuum Chamber****Introduction:**Two iron spheres with the same radius are visually identical from the outside. However, one sphere contains a hollow cavity inside, as demonstrated in the diagrams below. Both spheres are heated to a temperature of 350°C and suspended by thin cords from the ceiling of a vacuum chamber. The only means by which they can lose heat is through radiation.**Objective:**This exercise seeks to explore and explain the differences in heat radiation between the two spheres: 1. **Which sphere, if either, radiates more power?** 2. **Which sphere, if either, cools down the fastest?** Please provide explanations for each answer.**Diagram Explanation:**- The upper section of the image shows two iron spheres labeled "a" and "b" hanging from cords.- The lower section contains an "interior view" for each sphere: - Sphere "a" shows a cross-section with a hollow cavity. - Sphere "b" shows a solid cross-section.**Discussion Points:**- **Heat Radiation:** - The rate of radiation depends on the surface area and temperature but not on the volume. Since both spheres have the same outer surface area and are at the same temperature, they will radiate the same amount of power. - **Cooling Rate:** - The hollow sphere (sphere "a") has less mass than the solid sphere (sphere "b") due to the absence of material in the cavity. Thus, sphere "a" has less thermal energy to lose and will cool down faster despite radiating the same amount of power per unit time. Understanding these principles illustrates fundamental concepts of thermodynamics and radiative heat transfer. ### Formulas:#### Specific Heat:- \( c \equiv \frac{Q}{m \Delta T} \) (J/kg · °C)- \( Q = mc(T_f - T_i) \)#### Mixtures:- \( Q_{\text{cold}} = -Q_{\text{hot}} \)#### Latent Heat:- Phase change: \( Q = \pm mL \)#### Thermal Conductivity:- \( \frac{Q}{t} = \text{Power} = P = kA\frac{(T_h - T_c)}{L} \)#### Stefan's Law of Radiation:- \( P = \sigma A e T^4 \)

A) According to stefan's law of radiation :- Power radiated by a sphere depends only on it's surface…

Two iron spheres with the same radius look identical from the outside, but one has a hollow cavity on the inside (see below). They are both heated to a temperature of 350° C and suspended by a thin cord from the ceiling of a vacuum chamber. The only way they can lose heat is by radiation. (a) Which sphere, if either, will radiate more watts of power? Explain your answer (b) Which sphere, if either, will cool down the fastest? Explain your answer.

Two iron spheres with the same radius look identical from the outside, but one has a hollow cavity on the inside (see below). They are both heated to a temperature of 350° C and suspended by a thin cord from the ceiling of a vacuum chamber. The only way they can lose heat is by radiation. (a) Which sphere, if either, will radiate more watts of power? Explain your answer (b) Which sphere, if either, will cool down the fastest? Explain your answer.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: temperature

A: Given: Mass of the car = 1220 Kg Speed of the car = 32 m/s Mass of the iron = 30 Kg The kinetic…

Q: Imagine a person standing naked in a room at 19.1°C. The walls are well insulated, so they also are…

Q: An aluminum rod is 23.5 cm long at 20°C and has a mass of 350 g. If 10,500 J of energy is added to…

Q: On a hot day, the temperature of a 76,000 L swimming pool increases by 1.10°C. What is the net heat…

Q: A thermos bottle with a piston instead of a lid contains a fixed amount of gas. Because it is a…

A: A thermos bottle with a piston

Q: An insulated Thermos contains 190 cm³ of hot coffee at 85.0°C. You put in a 16.0 g ice cube at its…

Q: Six insulated containers hold 3,375 g of water at 24°C. A small copper cylinder is placed in each…

A: The objective of the question is to rank the containers according to the maximum temperature of the…

Q: Two metal rods, one silver and the other copper, are both attached to a steam chamber as shown in…

Q: The specific heat of copper is roughly three times as great as the specific heat of gold. Which of…

A: The specific heat capacity of a substance is the amount of energy required to raise the temperature…

Q: A 1.30 kg sample of water at 13.0°C is in a calorimeter. You drop a piece of steel with a mass of…

Q: Two rooms in the top floor of a building are heated by the same heating system such that an internal…

A: Step 1: We are given two rooms, A and B both heated to maintain an internal temperature of +22oC The…

Q: A 1,280 kg car going 29 m/s is brought to a stop using its brakes. Let's assume that a total of…

Q: On a hot day, the temperature of a 28,000 L swimming pool increases by 1.10°C. What is the net heat…

A: Given : Volume (V) = 28,000 L = 28 m3 Increase in temperature (∆T) = 1.10°C

Q: Assume that the efficiency of the portable solar panel shown in the figure is 19%. (a)(a) What is…

Q: 1. Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs…

Q: How much heat transfer is required to raise the temperature of a 0.32-kg aluminum pot containing 3.2…

Q: The human body, while at rest, produces heat energy at a rate of about 100 W. How much sweat (in g)…

Q: In an insulated vessel, 255 g of ice at 0°C is added to 585 g of water at 19.0°C. (Assume the latent…

Q: Consider the change in the internal energy of a system. -What is the change in the internal energy,…

A: Given data: Work done by the system (W) = 4.725×105 J Heat added (Qin) = 3.2×106 J Heat rejected…

Q: Two metal rods, one silver and the other copper, are both attached to a steam chamber as shown in…

Q: A certain monatomic gas inside a cylinder is at a temperature of 22°C. It takes 278 J of work done…

Q: A square steel bar of side length w= 0.13 m has a thermal conductivity of k= 14 J/(s •m.°C) and is…

A: Here given the sidelength of a bar is 0.13 m and length is 2.1 m. The temperature T1 = 78°C and…

Concept explainers

Energy transfer

The flow of energy from one region to another region is referred to as energy transfer. Since energy is quantitative; it must be transferred to a body or a material to work or to heat the system.

Molar Specific Heat

Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K-1)

Thermal Properties of Matter

Thermal energy is described as one of the form of heat energy which flows from one body of higher temperature to the other with the lower temperature when these two bodies are placed in contact to each other. Heat is described as the form of energy which is transferred between the two systems or in between the systems and their surrounding by the virtue of difference in temperature. Calorimetry is that branch of science which helps in measuring the changes which are taking place in the heat energy of a given body.

Question

**Title: Heat Radiation from Spheres in a Vacuum Chamber**

**Introduction:**

Two iron spheres with the same radius are visually identical from the outside. However, one sphere contains a hollow cavity inside, as demonstrated in the diagrams below. Both spheres are heated to a temperature of 350°C and suspended by thin cords from the ceiling of a vacuum chamber. The only means by which they can lose heat is through radiation.

**Objective:**

This exercise seeks to explore and explain the differences in heat radiation between the two spheres:

1. **Which sphere, if either, radiates more power?**
2. **Which sphere, if either, cools down the fastest?**

Please provide explanations for each answer.

**Diagram Explanation:**

- The upper section of the image shows two iron spheres labeled "a" and "b" hanging from cords.
- The lower section contains an "interior view" for each sphere:
- Sphere "a" shows a cross-section with a hollow cavity.
- Sphere "b" shows a solid cross-section.

**Discussion Points:**

- **Heat Radiation:**
- The rate of radiation depends on the surface area and temperature but not on the volume. Since both spheres have the same outer surface area and are at the same temperature, they will radiate the same amount of power.

- **Cooling Rate:**
- The hollow sphere (sphere "a") has less mass than the solid sphere (sphere "b") due to the absence of material in the cavity. Thus, sphere "a" has less thermal energy to lose and will cool down faster despite radiating the same amount of power per unit time.

Understanding these principles illustrates fundamental concepts of thermodynamics and radiative heat transfer.

### Formulas:

#### Specific Heat:
- \( c \equiv \frac{Q}{m \Delta T} \) (J/kg · °C)
- \( Q = mc(T_f - T_i) \)

#### Mixtures:
- \( Q_{\text{cold}} = -Q_{\text{hot}} \)

#### Latent Heat:
- Phase change: \( Q = \pm mL \)

#### Thermal Conductivity:
- \( \frac{Q}{t} = \text{Power} = P = kA\frac{(T_h - T_c)}{L} \)

#### Stefan's Law of Radiation:
- \( P = \sigma A e T^4 \)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Part A

VIEW

Part B

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Can you show me how to solve this?
An uninsulated container holds 3.5 mol of an ideal gas at an initial temperature of 300 K. The gas is compressed by a movable piston, and 500 J of work is done on the gas while being compressed. If the final temperature of the gas is 400 K, how much heat flows in or out of the gas during this process?
Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume so that its pressure drops from P₁ = 2.7 atm to P2 = 1.7 atm. Then the gas expands at constant pressure, from a volume of V₁ = 5.9 L to V₂ = 9.6 L, where the temperature reaches its original value. See the figure ( Figure 1). Figure P P₁ P2 σ P D HÅ AU = Value Units Submit Request Answer Part C 1 of 1 wwwww ? Calculate the total heat flow into or out of the gas. Express your answer to two significant figures and include the appropriate units. ☐ με Value Units Submit Request Answer
In testing a new drug, you heat a 0.5-kilogram sample using a hot plate. Assume no energy is lost in the process (i.e. the process is 100% efficient). The corresponding change in temperature and energy readings observed during the heating process are graphed as shown. Watch your units!!!! 16000 14000 12000 10000 8000 Q= 72 AT 6000 4000 2000 100 150 200 250 Change in Temperature (AT) [deg F] What is the specific heat capacity of the fluid in units of joules per gram kelvin? Hint: compare the trendline equation to the thermal energy equation. * A Energy (Q) [J]
When you turn your hot water on in the shower, it takes a bit for the water to get warm. Some of this is because the water in the pipe is cold but some of it is because the water from the hot water heater must heat the copper plumbing pipe itself. Copper has a specific heat of 0.39R. How much energy does it take to heat 2 kilograms of copper pipe from 70°F to 130°F? Report your answer in Joules. (Hint: Note that you'll need to convert kJ to J and F to K.)
Beryllium has roughly one-half the specific heat of liquid water (H20). Rank the quantities of energy input required to produce the following changes from the largest to the smallest. In your ranking, note any cases of equality. (Use only the symbols > or =, for example a>b=c) (a) raising the temperature of 1 kg of H,0 from 20°C to 26°C (b) raising the temperature of 2 kg of H20 from 20°C to 23°C (c) raising the temperature of 2 kg of H20 from 1°C to 4°C (d) raising the temperature of 2 kg of beryllium from O-1°C to 2°C (e) raising the temperature of 2 kg of H20 from O-1°C to 2°C
Can you please help me answer this?
Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and forth for a total of 10 rubs, at a distance of 7.50 cm per rub, and with a frictional force of 50.0 N, what is the temperature increase in degrees Celsius? The mass of tissue warmed is only 0.100 kg, mostly in the palms and fingers.
An ice block of mass 1.2000000000000002 kg at an initial temperature of –11 ∘C is put into a copper pot of mass 2.5 kg containing 4.3 L of water at 21 ∘C. If you heat up the pot, what is the amount of energy (in J) you need to convert all the ice and the water into steam? (Assume that no energy is lost from the system.) You may need some or all of the following constants: The specific heat of ice is 2200 J/kg ∘C, the specific heat of copper is 386 J/kg ∘C and the specific heat of water is 4186 J/kg ∘C. The latent heat of fusion of ice is 334000 J/kg and the heat of vaporization for water is 2256000 J/kg .
Your car’s radiator is made of steel and is filled with coolant. You fill the radiator to the very top with coolant, then drive off without remembering to replace the cap. As the coolant and steel radiator heats up, will the level of coolant drop or rise and overflow? why? what is a radiator is and what purpose does it serves in a car? Here is a good start: https://youtu.be/y5p31F_dVJU