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A 0.35 kg piece of copper at a temperature of 151 degrees Celsius is dumped into 500 ml of water at a temperature of 18 degrees Celsius. What is the final equilibrium temperature?

a) 34.51°C
b) 43.26°C
c) 52.13°C
d) 62.94°C

Answer :

Final answer:

To find the final equilibrium temperature when copper is placed in water, we apply the heat transfer equation, taking into account the mass and specific heat capacities of both substances, and solve for the temperature where heat lost by copper equals heat gained by water.

Explanation:

To calculate the final equilibrium temperature when a 0.35 kg piece of copper at 151 degrees Celsius is placed in 500 ml of water at 18 degrees Celsius, we can use the concept of heat transfer and the principle of conservation of energy. In this case, the heat lost by the copper will be equal to the heat gained by the water since there's no heat transfer to the surroundings.

We use the formula:
Q = mcΔT,

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

For water, the specific heat capacity (cwater) is approximately 4.18 J/g°C, and for copper, (ccopper) it is roughly 0.385 J/g°C. The mass of the water can be found by converting the volume to mass (as 1 ml of water roughly equals 1 g), so we have 500 g of water.

Let's denote the final equilibrium temperature as T f. The heat lost by the copper will be equal to the heat gained by the water:

(mcopperccopper(Tinitial,copper-T f)) = (mwatercwater(T f-Tinitial,water))

0.35*1000*0.385*(151-T f) = 500*4.18*( T f-18)

We solve this equation for T f to find the final temperature.

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