20. Heat and Temperature

A cube has an edge length of $10$ centimeters. What is its volume in cubic centimeters (${\mathrm{cm}}^3$)?

What is the volume of a sphere with a radius of $41$ inches, rounded to the nearest tenth of a cubic inch? (Use $\pi$ ≈ $3.1416$)

A cube has an edge length of $13$ feet. What is its volume?

It is observed that 55.50 mL of water at 20°C completely fills a container to the brim. When the container and the water are heated to 60°C, 0.35 g of water is lost.

(a) What is the coefficient of volume expansion of the container?

(b) What is the most likely material of the container? Density of water at 60°C is 0.98324 g/mL.

A cube has an edge length of $11m$. What is its volume in cubic meters ($m^3$)?

The density of gasoline at 0°C is 0.68 x 10³ kg/m³. (a) What is the density on a hot day, when the temperature is 33°C? (b) What is the percent change in density?

A glass is filled to the brim with 450.0 mL of water, all at 100.0°C. If the temperature of glass and water is decreased to 20.0°C, how much water could be added to the glass?

A uniform rectangular plate of length ℓ and width ω has a coefficient of linear expansion α. Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change ∆T is ∆A = 2αℓω ∆T. See Fig. 17–21.

A Pyrex measuring cup was calibrated at normal room temperature. How much error will be made in a recipe calling for 375 mL of cool water, if the water and the cup are hot, at 95°C, instead of at room temperature? Neglect the glass expansion.

Given a solid cylinder with initial radius $r$, height $h$, and a coefficient of volume expansion $\beta$, what is the new volume of the cylinder after a temperature increase of $\Delta T$?

Consider three capacitors, of capacitance 3100 pF, 5800 pF, and 0.0100 μF. What maximum and minimum capacitance can you form from these? How do you make the connection in each case?

A steel tank is completely filled with 1.90 m³ of ethanol when both the tank and the ethanol are at 32.0°C. When the tank and its contents have cooled to 18.0°C, what additional volume of ethanol can be put into the tank?

The density of water at 4°C is 1.00 x 10³ kg / m³. What is water’s density at 94°C? Assume a constant coefficient of volume expansion.

At a given latitude, ocean water in the so-called mixed layer (from the surface to a depth of about 50 m) is at approximately the same temperature due to the mixing action of waves. Assume that because of global warming, the temperature of the mixed layer is everywhere increased by 0.5°C, while the temperature of the deeper portions of the ocean remains unchanged. Estimate the resulting rise in sea level. The ocean covers about 70% of the Earth’s surface.

In an alcohol-in-glass thermometer, the alcohol column has length 12.61 cm at 0.0°C and length 22.79 cm at 100.0°C. What is the temperature if the column has length 14.40 cm?