Fig. 10.1 shows a sealed flask containing air connected to a pressure gauge. The flask is heated in a water bath. The air in the flask is initially at 27 °C...
Question 1 Report
Fig. 10.1 shows a sealed flask containing air connected to a pressure gauge. The flask is heated in a water bath.
The air in the flask is initially at 27 °C and a pressure of 1.0 × 10⁵ Pa.
(a) Convert 27 °C to kelvin. [1]
(b) The water bath is heated until the air reaches 127 °C. Calculate the new pressure of the air in the flask. [3]
(c) Explain, in terms of particles, why the pressure of the air increases when the temperature rises. [2]
(d) State what would happen to the flask if the temperature is raised much further. Explain your answer. [1]
Answer Details
(a) To convert Celsius to kelvin, add 273:
\(T = 27 + 273 = 300\text{ K}\) [1]
(b) First convert the new temperature to kelvin:
\(T_2 = 127 + 273 = 400\text{ K}\) [1]
The flask is sealed (constant volume), so use the pressure-temperature law: \(\dfrac{p_1}{T_1} = \dfrac{p_2}{T_2}\)
Rearranging: \(p_2 = p_1 \times \dfrac{T_2}{T_1} = 1.0 \times 10^5 \times \dfrac{400}{300}\) [1]
\(p_2 = 1.33 \times 10^5\text{ Pa}\) (or \(1.3 \times 10^5\text{ Pa}\)) [1]
The pressure increases because the temperature increased. Since the volume cannot change (sealed flask), all the extra kinetic energy goes into increasing the force and frequency of particle collisions with the walls.
(c) At a higher temperature, the gas particles move faster and have more kinetic energy. [1] They collide with the walls of the flask more frequently and with greater force, so the total force per unit area (pressure) on the walls increases. [1]
(d) The flask could crack or explode because the pressure inside becomes too great for the glass to withstand. [1]
Glass has a limited tensile strength. As the temperature continues to rise, the internal pressure keeps increasing, and eventually the glass fails catastrophically.
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