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- Materials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount ∆T, then the rod's length approximately changes by ∆L = ∝Lo∆T, where a is the thermal expansion coefficient and ∆ T is not an extreme temperature change. For steel, ∝ = 1.24 X 10- 5 0 c- 1. (a) A steel rod has length Lo = 40 cm at To = 40°C. Find its length at T = 90°C. (b) Find its length at T = 50°C if its length at To= 100°C is 65 cm. ( c) Express length L as a function of T if Lo = 65 cm at To = 100°C.An electric heater producing 260 W of heat is used to warm up a room containing 7 m3 of air. If we assume the room is perfectly sealed and there is no heat loss through the room boundaries, such that all of the heater output goes into increasing the air temperature, how long will it take to heat up the air in the room from 5.0 °C to 24.1 °C? Give your answer to the nearest minute and assume that the specific volume (v = 0.85 m3/kg) and specific heat capacity at constant volume (cv = 1.005 kJ/(kg K)) remain constant throughout the heating process.4-A spherical interplanetary probe of 0.5 m diameter contains electronics thatdissipate 150 W. If the probe surface has an emissivity of 0.8 and the probe does not receive radiation from other surfaces, as, for example from the sun, what is the probe surface temperature?
- Consider the vertical heat sink (see the figure) used to cool a surface at 70 0C. The room temperature is 30 0C. The dimensions are given as (H=2 cm, L=5 cm, t=1 mm, W=15 cm). If the space between the fins is arranged so that the heat transfer rate is maximum, what is the heat transfer rate from the heat sink? Properties of air: ρ=1 kg/m3, k=0.03 W/mK, ν=1.5x10-5 m2/s, cp=1 kJ/kg0C, Pr=0.7Air is trapped in the piston in the cylinder. A spring is connected to the upper portion of the piston and returns the force upon compression by the F = -kx equation. k = 50,000 N/m and x is the distance traveled when the piston is compressed. The piston is located 10 cm above the bottom of the cylinder with a cross-sectional area of 0.01 m2 and an initial condition of 1 bar and 25°C. In this state, the spring does not apply force to the piston. At this time, the system was reversibly heated and the temperature rose to 100°C. (a) What happened was (b) What is the heat transferred?A mass of ice at -7 C is needed to cool 224 kg of vegetables (Cp = 3.35 KJ /kg.K )in a bunker for 24 hours. The initial temperature of the vegetables is assumed to be 29 C . It is also assumed that the average temperature in the bunker is 7C within the 24 -hour period . If the heat gained per hour in the bunker is 25% of the heat removed to the vegetables from 29 C to 7C, what would be the required mass of ice ? show t-s diagram
- 1. Most bridges contain interlocking steel grates (α steel = 1.2 x 10 - 5 ºC -1 ) that allow the bridge toexpand and contract with the changes in temperature. The Golden Gate Bridge in San Francisco isabout 1350 meters long.(A) The seasonal temperature variation in San Francisco ranges from about 0ºC to 30ºC. Howmuch will the bridge expand between these two extremes?(B) What percent of the length of a subcompact automobile, 2.5 meters, does this gaprepresent?2. Selena has a fire in her fireplace to warm her 20ºC apartment. She realizes that she hasaccidentally left the iron poker (α iron = 1.2 x 10 -5 ºC -1 ) in the fire. How hot is the fire if the 0.60-meter poker lengthens 0.30 cm?3. Just before midnight, when the air temperature of 10.0ºC, Karl stops and fills the 0.0600 m 3 gastank in his car. At noon the next day, when the temperature has risen to 32ºC, Karl finds a puddle ofgasoline (βgas = 3 x 10 -4 ºC -1 ) beneath his car.(A) How much gasoline spilled out of Karl's car?…A solid rectangular parallelepiped is made of aluminum and is initially at 20 C. The base is a 2 cm by 3 cm rectangle and the height of the parallelepiped is 5 cm. The parallelepiped is now dropped into hot oil at 150 C. Find: a) the temperature of point P and b) the temperature of the center of the parallelepiped after 2 min of exposure to hot oil. Point P is located 1 cm above the center plane and1 cm from each side.A steel bar 7 cm long is welded end to end to a copper bar 21 cm long. Both bars are insulated perfectly on their sides. Each bar has a square cross-section 2.0 cm on a side. The free end of the steel bar is maintained at 100 deg C by placing it in contact with steam, and the free end of the copper bar is maintained at 0 deg C by placing it in contact with ice. Find the temperature (in deg C) at the junction of the two bars. kst = 50.2 W/m.K; kcu = 385 W/m.K Round your answer to 2 decimal places. (Topic: Heat Transfer, Waves, and Oscillations)
- What quantity of heat is required to raise the temperature of 20 L of water from 25 °C to 50 °C.? Given: specific heat of water is 4.18 J g-1 K-1. Show the relevant mathematical equation and all steps of your work. Express your final answer in kJ.Example 2: Double-pane window, each window have: Height = 0.8 m Width 1.5 m Thickness = 4 mm k (glass) = 0.78 W/m.K separation between two glasses (air) = 10 mm k (air) = 0.026 W/m.K Temperature of inner surface = 20°C Temperature of outer surface = -10°C Convection heat transfer coefficient on the inner surface h1= 10 W/m2·°C Convection heat transfer coefficient on the outer surface h2= 40 W/m2·°C Determine the heat transfer through the window?3. The heat flux (from outside to inside) across an insulating wall with thermal conductivity, K= 0.04 W/m-K and thickness 0.16m is 10 W/m2. The temperature of the inside wall is - 5°C. The outside wall temperature is _____. (avoid rounding off during intermediate steps, but only on final answers to four decimal places.)