Volume Thermal Expansion Practice Problems

A student completely filled a quartz Erlenmeyer flask of volume 250 ml with glycerin liquid. The flask and the glycerin are in thermal equilibrium at 25 °C. The flask was placed in a refrigerator at 10 °C. At 10 °C, how much more glycerin can the student pour into the flask?

The shot put is an event involving throwing a heavy, spherical ball as far as possible. The shot is made of brass and has a diameter of 115 mm at 20 °C. Find the change in the shot volume (ΔV) if it is stored in the summer at a location where the temperature is 50°C.

A scientist uses a thermometer containing isopropyl alcohol with a volumetric thermal expansion coefficient (β) of 7.9 x 10^-4 K^-1 to monitor a temperature-sensitive experiment. The thermometer has a 0.50 mm diameter capillary tube and an 8 mm diameter spherical bulb. At 0°C, the alcohol column is 40 mm above the bulb. Determine the temperature when the column reaches 145 mm, considering the glass expansion is negligible compared to the alcohol.

You have a 15 cm high copper cylinder with a diameter of 5 cm along a plane at right angles to the axis of the cylinder. The piece behaves as a two-dimensional circular object. The initial temperature of the piece is 25°C. Calculate the percentage change in volume of the cylindrical piece when heated to 75°C. Assume the coefficient of volumetric expansion for copper is 51×10⁻⁶/°C.

A certain type of oil has a density of 2.0 × 10³ kg/m³ at 5 °C. Calculate the density of this oil at 96 °C. Assume the volume expansion coefficient is 240 ×10^-6 °C^-1.

A metal container holds exactly one liter (1000 ml) of mineral oil at a temperature of 150°C when filled to its maximum capacity without spilling over the edge. How much more or less oil could fit into this container if cooled to room temperature (25°C)?

A scientist is measuring a 450 ml sample of ethanol that is required for an experiment using a graduated cylinder that is calibrated at a temperature of 25°C. Calculate the error in measurement if the ethanol and cylinder are at a temperature of 45°C, assuming that there is no expansion of the cylinder. [Hint: the coefficient of volume expansion for ethanol is β = 0.0011 /°C.]

A tank contains mercury that has an initial temperature of 20°C and has a known density of 13.6 × 10³ kg/m³. Calculate its new density value and the percent change in the density when the temperature rises to 45°C, given that mercury's coefficient of volumetric expansion is 0.000181 /°C.

A cylindrical tank of volume 1.50 × 10² mL was initially full of glycerol at a temperature of 15.0 °C. After heating the system to 45.0 °C, it is found that 2.63 g of glycerol has overflowed. (i) Given that the coefficient of volume expansion of glycerol is 5.10 × 10^-4/°C and its density at 45.0 °C is approximately 1.23 g/mL, calculate the coefficient of volume expansion for the tank. (ii) Using the table below, determine what the tank is most likely to be made of.

The change in the density 𝜌 of a substance, when the temperature changes by Δ𝑇, is given by the equation $\Delta \rho=-\beta \rho \Delta T$. In a climate control experiment, the coefficient of volume expansion for a certain liquid substance in the temperature range from 0.0°C to about 20.0°C is given approximately by $\beta=a+b T+c T^{2}$, where $a=-6.43 \times 10^{-5}\left({ }^{\circ} C\right)^{-1}, b=1.70 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-2}$, and $c=-2.02\times 10^{-7}\left(^{\circ }C\right)^{-3}$. Using this formula, determine the temperature at which this liquid substance has its greatest density within the given temperature range.

A freshwater lake has a uniform temperature layer from the surface of the water to a depth of about 30 m. Due to prolonged summer heat, the temperature of this layer rises by 0.3 °C across the entire layer while deeper parts remain at a constant temperature. Calculate the rise in water level in the summer, assuming that the coefficient of volume expansion of water is 2.1 × 10^-4/C°.

What is the temperature in a mercury-in-glass thermometer if the mercury column has a length of 12.5 cm, given that the column length is 10.0 cm at 0.0°C and 20.0 cm at 100.0°C?

You have a metallic rectangular plate with a length of l and a width of w at a specific temperature. Study the change in the area of this plate under a change in temperature ΔT while neglecting the effect of all minimal quantities. The coefficient of linear expansion is α.

The distance between the surface of the olive oil and the bottom of the cork in an olive oil bottle is called the "headspace height," and is typically 2.0 cm for a 1.0-liter bottle filled at 25.0°C. Olive oil bottles are designed with a small air space left in the bottle's cylindrically shaped neck (inner diameter 25.0 mm) to accommodate for the oil's significant thermal expansion. Due to its properties, olive oil's coefficient of volume expansion is approximately 700×10⁻⁶/C°; in comparison, the thermal expansion of glass can be neglected. Estimate the headspace height if the bottle is kept at 5.0°C.

An engineer designs a circuit and has three capacitors available: one with a capacitance of 2200 pF, another with 4700 pF, and the last with 0.0150 μF. Determine the maximum and minimum capacitance you can achieve with these capacitors, and explain how you would connect them to obtain each value.