Liquid helium, with a boiling point of 4.2 K, is used in ultralow-temperature experiments and also for cooling the superconducting magnets used in MRI imaging in medicine. Storing liquid helium so far below room temperature is a challenge because even a small 'heat leak' will boil the helium away. A standard helium dewar, shown in FIGURE P19.67, has an inner stainless-steel cylinder filled with liquid helium surrounded by an outer cylindrical shell filled with liquid nitrogen at –196°C. The space between is a vacuum. The small structural supports have very low thermal conductivity, so you can assume that radiation is the only heat transfer between the helium and its surroundings. Suppose the helium cylinder is 16 cm in diameter and 30 cm tall and that all walls have an emissivity of 0.25. The density of liquid helium is 125 kg/m³ and its heat of vaporization is 2.1×10⁴ J/kg. What is the mass of helium in the filled cylinder?

Suppose that the rod in Fig. $17.24$a is made of copper, is $45.0$ cm long, and has a cross-sectional area of $1.25$ cm² . Let $TH=100.0$°C and $TC=0.0$°C. What is the final steady-state temperature gradient along the rod?

A carpenter builds an exterior house wall with a layer of wood $3.0$ cm thick on the outside and a layer of Styrofoam insulation $2.2$ cm thick on the inside wall surface. The wood has $k=0.080W/m\cdot K$ , and the Styrofoam has $k=0.027W/m\cdot K$. The interior surface temperature is $19.0$°C, and the exterior surface temperature is $-10.0$°C. What is the temperature at the plane where the wood meets the Styrofoam?

A carpenter builds an exterior house wall with a layer of wood $3.0$ cm thick on the outside and a layer of Styrofoam insulation $2.2$ cm thick on the inside wall surface. The wood has $k=0.080\,W/m\cdot K$ , and the Styrofoam has $k=0.027\,W/m\cdot K$. The interior surface temperature is $19.0$°C, and the exterior surface temperature is $-10.0$°C. What is the rate of heat flow per square meter through this wall?

Most stars are main-sequence stars, a group of stars for which size, mass, surface temperature, and radiated power are closely related. The sun, for instance, is a yellow main-sequence star with a surface temperature of 5800 K. For a main-sequence star whose mass M is more than twice that of the sun, the total radiated power, relative to the sun, is approximately P/P_sun=1.5(M/M_sun)^3.5. The star Regulus A is a bluish main-sequence star with mass 3.8M_sun and radius 3.1R_sun. What is the surface temperature of Regulus A?

You are boiling pasta and absentmindedly grab a copper stirring spoon rather than your wooden spoon. The copper spoon has a 20 mm ×1.5 mm rectangular cross section, and the distance from the boiling water to your 35°C hand is 18 cm. How long does it take the spoon to transfer 25 J of energy to your hand?

The ends of a 20-cm-long, 2.0-cm-diameter rod are maintained at 0°C and 100°C by immersion in an ice-water bath and boiling water. Heat is conducted through the rod at 4.5×10⁴ J per hour. Of what material is the rod made?

A 2.0-cm-diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of 2.0 μm. How much power does the sphere radiate? Assume e=1 .

A ceramic cube 3.0 cm on each side radiates heat at 630 W. At what wavelength, in μm, does its emission spectrum peak? Assume e=1.