**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

Similar questions

Electronics and inhabitants of the International Space Station generate a significant amount of thermal energy that the station must get rid of. The only way that the station can exhaust thermal energy is by radiation, which it does using thin, 1.8-m-by- 3.6-m panels that have a working temperature of about 6°C. How much power is radiated from each panel? Assume that thepanels are in the shade so that the absorbed radiation will be negligible. Assume that the emissivity of the panels is 1.0.
Consider a thin round plate at 350K with a radius of 18 cm is placed on a very large and very thick table of conductivity k = 1.6 W/mK. The plate has an emissivity of 0.6 and the temperature of the surrounding air and the table and the large room walls is 298 K. At this time, (a) How much heat (in W) is leaving via radiation? (b) How much heat (in W) is leaving via convection? (c) How much heat (in W) is leaving via conduction?
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?
WITH THE CONCEPT OF HEAT TRANSFER, ANSWER THE FOLLOWING AND SHOW THE COMPLETE SOLUTION: A 10.0-cm long steel rod is welded end to end to a 20.0-cm long copper rod of the same cross-sectional area. The thermal conductivities of steel and copper are 50.2 W/m·K and 385 W/m·K, respectively. The steel end is kept at 100°C while the copper end is kept at 0°C. What is the steady-state temperature at the interface connecting the two rods?
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 .