An ice chest at a beach party contains 12 cans of soda at 4.16 °C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kg C°). Someone adds a 8.48-kg watermelon at 25.7 °C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon in degrees Celsius.

Question

An ice chest at a beach party contains 12 cans of soda at 4.16 °C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kg C°). Someone adds a 8.48-kg watermelon at 25.7 °C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon in degrees Celsius.

Answer 1

To determine the final temperature T of the soda and watermelon, we need to use the principle of heat transfer.

The heat transfer is given by the equation:

Q = m * c * ΔT

where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

For the soda, we have:

Q_soda = m_soda * c_soda * ΔT_soda

For the watermelon, we have:

Q_watermelon = m_watermelon * c_watermelon * ΔT_watermelon

Since we want to find the final temperature at which the two reach thermal equilibrium, we can assume that the final heat transferred by the soda is equal to the final heat transferred by the watermelon:

Q_soda = Q_watermelon

Now, let's calculate the heat transferred by the soda and watermelon.

For the soda, we have:
m_soda = 12 cans * 0.35 kg/can = 4.2 kg
c_soda = 3800 J/(kg °C)
ΔT_soda = T - 4.16 °C

For the watermelon, we have:
m_watermelon = 8.48 kg
c_watermelon ≈ c_water ≈ 4186 J/(kg °C) (specific heat capacity of water)
ΔT_watermelon = T - 25.7 °C

Since Q_soda = Q_watermelon, we can set up the equation:

m_soda * c_soda * ΔT_soda = m_watermelon * c_watermelon * ΔT_watermelon

Substituting the given values:

4.2 kg * 3800 J/(kg °C) * (T - 4.16 °C) = 8.48 kg * 4186 J/(kg °C) * (T - 25.7 °C)

Now, solve the equation for T by simplifying and rearranging terms:

4.2 * 3800 * T - 4.2 * 3800 * 4.16 = 8.48 * 4186 * T - 8.48 * 4186 * 25.7

(4.2 * 3800 - 8.48 * 4186) * T = 8.48 * 4186 * 25.7 - 4.2 * 3800 * 4.16

T = (8.48 * 4186 * 25.7 - 4.2 * 3800 * 4.16) / (4.2 * 3800 - 8.48 * 4186)

Calculating this expression will give you the final temperature T at which the soda and watermelon will reach thermal equilibrium.