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State two factors that affect the rate of evaporation of a liquid. Explain the term latent heat. Explain each of the following phenomena: On a dry day, water in a clay pot is cooler than water in a rubber container. Cooking of food is faster in a pressure cooker than in an ordinary pot.

Physics

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Answer

e

352 °C\text{352 °C}

Step-by-step solution

4 steps

Part e· 4 steps

Calculate its temperature.

  1. Convert the initial temperature to Kelvin.

    The relationship between the speed of sound (vv) and absolute temperature (TT) is given by v∝Tv \propto \sqrt{T}.
    Given v1=240 m/sv_1 = 240 \text{ m/s} at T1=102 °CT_1 = 102 \text{ °C}.

    T1=102 °C+273.15=375.15 KT_1 = 102 \text{ °C} + 273.15 = 375.15 \text{ K}
  2. Set up the ratio of speeds and temperatures.

    We are given v2=310 m/sv_2 = 310 \text{ m/s} and need to find T2T_2.

    v1v2=T1T2\frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}} 240 m/s310 m/s=375.15 KT2\frac{240 \text{ m/s}}{310 \text{ m/s}} = \sqrt{\frac{375.15 \text{ K}}{T_2}}
  3. Solve for T2T_2.

    Square both sides of the equation:

    (240310)2=375.15T2(2431)2=375.15T2576961=375.15T2T2=375.15 K×961576T2≈625.06 K\left(\frac{240}{310}\right)^2 = \frac{375.15}{T_2} \\ \left(\frac{24}{31}\right)^2 = \frac{375.15}{T_2} \\ \frac{576}{961} = \frac{375.15}{T_2} \\ T_2 = 375.15 \text{ K} \times \frac{961}{576} \\ T_2 \approx 625.06 \text{ K}
  4. Convert T2T_2 back to Celsius.

    T2 (°C)=625.06 K−273.15T2 (°C)≈351.91 °CT_2 \text{ (°C)} = 625.06 \text{ K} - 273.15 \\ T_2 \text{ (°C)} \approx 351.91 \text{ °C}

    The temperature is approximately 352 °C\boxed{\text{352 °C}}.

    11. (a) State two factors that affect the rate of evaporation of a liquid.

    1. Temperature: A higher temperature increases the kinetic energy of liquid molecules, allowing more of them to escape into the vapor phase.
    2. Surface area: A larger exposed surface area allows more molecules to escape from the liquid's surface per unit time.

    11. (b) Explain the term latent heat.

    Latent heat is the energy absorbed or released by a substance during a phase change (e.g., melting, boiling, freezing, condensation) without a change in its temperature. This energy is used to break or form intermolecular bonds, changing the state of matter rather than increasing or decreasing its kinetic energy.

    11. (c) Explain each of the following phenomena:

Part e(i)

On a dry day, water in a clay pot is cooler than water in a rubber container.

Clay pots are porous, allowing water to seep through to the outer surface. On a dry day, this water evaporates from the exterior of the pot. Evaporation is a cooling process because the most energetic water molecules absorb latent heat of vaporization from the remaining water and the pot itself to escape as vapor, thus lowering the temperature of the water inside. Rubber containers are non-porous, preventing this evaporative cooling.

Part e(ii)

Cooking of food is faster in a pressure cooker than in an ordinary pot.

In a pressure cooker, the sealed lid traps steam, which increases the pressure inside the cooker. This elevated pressure raises the boiling point of water above its normal 100 °C. Since the water boils at a higher temperature, the food cooks faster because chemical reactions involved in cooking proceed more rapidly at higher temperatures.

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