Question 1

Calculate the rate of heat transfer from a 1.5 m × 1.0 m window frame that is made of aluminum. The thickness of the frame is 1 mm and measures 3 cm from inside to outside. The inside room temperature is 25°C and outside temperature is 0°C.

Accepted Answer

The rate of heat transfer through a material is given by the equation:Q = k * A * (T1 - T2) / dwhere:Q is the rate of heat transfer in wattsk is the thermal conductivity of the material in W/m-KA is the area of the material in square metersT1 is the temperature on one side of the material in KelvinT2 is the temperature on the other side of the material in Kelvind is the thickness of the material in metersIn this problem, we are given the following information:k = 237 W/m-K (for aluminum)A = 1.5 m * 1.0 m = 1.5 square metersT1 = 25°C = 298 KT2 = 0°C = 273 Kd = 1 mm = 0.001 mPlugging these values into the equation, we get:Q = 237 W/m-K * 1.5 square meters * (298 K - 273 K) / 0.001 mQ = 988 WTherefore, the rate of heat transfer through the window frame is 988 W.

Question 2

If a piece of iron is exposed to the sun, its temperature rises until

Accepted Answer

When a piece of iron is exposed to the sun, its temperature increases until the rate at which it absorbs heat from the sun equals the rate at which it loses heat to its surroundings. This is a state of thermal equilibrium.

Question 3

A solid sphere at temperature T radiates energy at a rate of R J/s. If the radius of the sphere were doubled its temperature remains at T), then the rate of radiating energy would go up by a factor of

Accepted Answer

The rate of radiating energy (R) is given by the Stefan-Boltzmann law:

R = σT^4
where σ is a constant.

If the radius is doubled, the surface area of the sphere increases by a factor of 4 (A ∝ r^2). Since the energy radiated is proportional to the surface area of the sphere, the new rate of radiating energy (R') is:

R' = R × (new surface area/old surface area)
R' = R × (4 × old surface area/old surface area)
R' = 4R

Therefore, the rate of radiating energy would go up by a factor of 4.

Question 4

You are trying to decide what the change in heat loss would be if you put a 100 cm × 150 cm and 5-mm thick glass window in an outside wall. The thickness of the wall is 15 cm. If the thermal conductivities of the glass and wall are 0.90 W/m·K and 0.15 W/m·K, respectively, calculate the difference in heat loss through thermal conductivity with and without the window when the outside temperature is −10°C and the inside temperature is 15°C.

Accepted Answer

The answer of You are trying to decide what the...

Question 5

An object at temperature 227°C radiates energy at a net rate of R J/s.By what factor would the net rate of energy loss increase if the same object were at a temperature of 427°C? Assume the surrounding temperature is 0°C.

Accepted Answer

The rate of energy radiation is proportional to the fourth power of the absolute temperature (Stefan-Boltzmann law). Converting temperatures to Kelvin: 227°C = 500K and 427°C = 700K. The factor increase is (700/500)^4 = 4.1.

Question 6

The temperature gradient in a wall is 80^oC/cm, and the thermal conductivity of this wall is 4.0 × 10^-³ cal/s · cm · C^o. The amount of heat conducted per minute per square centimeter through this wall is approximately

Accepted Answer

The heat conducted per second per square centimeter is given by Fourier's law: q = k * (dT/dx). Here, q = 4.0 × 10^-3 cal/s·cm·°C * 80 °C/cm = 0.32 cal/s·cm². For one minute (60 seconds), the heat conducted is 0.32 cal/s·cm² * 60 s = 19.2 cal/cm², approximately 19 cal.

Quiz 14: Thermodynamics I

Calculate the rate of heat transfer from a 1.5 m × 1.0 m window frame that is made of aluminum. The thickness of the frame is 1 mm and measures 3 cm from inside to outside. The inside room temperature is 25°C and outside temperature is 0°C.

If a piece of iron is exposed to the sun, its temperature rises until

A solid sphere at temperature T radiates energy at a rate of R J/s. If the radius of the sphere were doubled its temperature remains at T) , then the rate of radiating energy would go up by a factor of

An object at temperature 227°C radiates energy at a net rate of R J/s.By what factor would the net rate of energy loss increase if the same object were at a temperature of 427°C? Assume the surrounding temperature is 0°C.

The temperature gradient in a wall is 80^oC/cm, and the thermal conductivity of this wall is 4.0 × 10^-³ cal/s · cm · C^o. The amount of heat conducted per minute per square centimeter through this wall is approximately

Quiz 14: Thermodynamics I

Calculate the rate of heat transfer from a 1.5 m × 1.0 m window frame that is made of aluminum. The thickness of the frame is 1 mm and measures 3 cm from inside to outside. The inside room temperature is 25°C and outside temperature is 0°C.

If a piece of iron is exposed to the sun, its temperature rises until

A solid sphere at temperature T radiates energy at a rate of R J/s. If the radius of the sphere were doubled its temperature remains at T) , then the rate of radiating energy would go up by a factor of

An object at temperature 227°C radiates energy at a net rate of R J/s.By what factor would the net rate of energy loss increase if the same object were at a temperature of 427°C? Assume the surrounding temperature is 0°C.

The temperature gradient in a wall is 80oC/cm, and the thermal conductivity of this wall is 4.0 × 10-3 cal/s · cm · Co. The amount of heat conducted per minute per square centimeter through this wall is approximately

The temperature gradient in a wall is 80^oC/cm, and the thermal conductivity of this wall is 4.0 × 10^-³ cal/s · cm · C^o. The amount of heat conducted per minute per square centimeter through this wall is approximately