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A 1.08 kW heater is used to convert 100 g of water at 100 °C into steam. How long will it take?

Physics

ScanSolve AI Answer

Answer

210 s\text{210 s}

Step-by-step solution

5 steps
  1. Identify the given values and the required physical constant.

    The power of the heater is P=1.08 kWP = 1.08 \text{ kW}.
    The mass of steam to be produced is m=100 gm = 100 \text{ g}.
    The water is already at 100 °C100 \text{ °C}, so we only need to consider the latent heat of vaporization.
    The latent heat of vaporization of water (LvL_v) is approximately 2.26×106 J/kg2.26 \times 10^6 \text{ J/kg}.

  2. Convert the given values to SI units.

    P=1.08 kW=1.08×1000 W=1080 WP = 1.08 \text{ kW} = 1.08 \times 1000 \text{ W} = 1080 \text{ W} m=100 g=100×10−3 kg=0.1 kgm = 100 \text{ g} = 100 \times 10^{-3} \text{ kg} = 0.1 \text{ kg} Lv=2.26×106 J/kgL_v = 2.26 \times 10^6 \text{ J/kg}
  3. Calculate the total heat energy required to convert 100 g100 \text{ g} of water at 100 °C100 \text{ °C} into steam.

    The heat energy QQ required for vaporization is given by the formula Q=mLvQ = m L_v.

    Q=(0.1 kg)×(2.26×106 J/kg)Q = (0.1 \text{ kg}) \times (2.26 \times 10^6 \text{ J/kg}) Q=2.26×105 JQ = 2.26 \times 10^5 \text{ J}
  4. Calculate the time taken for the heater to supply this amount of energy.

    The power PP of the heater is the rate at which it supplies energy, so P=QtP = \frac{Q}{t}, where tt is the time.
    Rearranging for tt:

    t=QPt = \frac{Q}{P} t=2.26×105 J1080 Wt = \frac{2.26 \times 10^5 \text{ J}}{1080 \text{ W}} t=2260001080 st = \frac{226000}{1080} \text{ s} t≈209.26 st \approx 209.26 \text{ s}
  5. Compare the calculated time with the given options.

    The calculated time is approximately 209.26 s209.26 \text{ s}, which is closest to 210 s210 \text{ s}.

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