High School

A cup of hot tea at 85ºC is placed in a room where the ambient air temperature is 30ºC. The surface area of the tea exposed to air is 0.068 m², and the convective heat transfer coefficient between the tea surface and the air is 10 W/(m²·K).

Calculate the rate of heat transfer from the tea to the surrounding air.

Answer :

The parameters, the rate of heat transfer is 37.4 Watts.

To solve the problem of calculating the rate of heat transfer from a cup of hot tea to the surrounding air, we use the formula for convective heat transfer:

Q = hA(Tsurface - Tambient)

Where:

  • Q is the rate of heat transfer (in Watts)
  • h is the convective heat transfer coefficient (in W/(m²·K)), which is given as 10 W/(m²·K)
  • A is the surface area of the tea exposed to air, which is 0.068 m²
  • Tsurface is the temperature of the tea, which is 85°C
  • Tambient is the ambient air temperature, which is 30°C

First, calculate the temperature difference (ΔT):

  • ΔT = Tsurface - Tambient = 85°C - 30°C = 55°C

Now, plug the values into the heat transfer equation:

  • Q = hAΔT = 10 W/(m²·K) × 0.068 m² × 55 K = 37.4 W

Thus, the rate of heat transfer from the hot tea to the surrounding air is 37.4 Watts.

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