Question

A 248-g piece of copper is dropped into 390 mL of water at 22.6 °C. The final temperature of the water was measured as 39.9 °C. Calculate the initial temperature of the piece of copper. Assume that all heat transfer occurs between the copper and the water. Remember, the density of water is 1.0 g/m

Answer 1

Answer:

335°C

Explanation:

Heat gained or lost is:

q = m C ΔT

where m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.

Heat gained by the water = heat lost by the copper

mw Cw ΔTw = mc Cc ΔTc

The water and copper reach the same final temperature, so:

mw Cw (T - Tw) = mc Cc (Tc - T)

Given:

mw = 390 g

Cw = 4.186 J/g/°C

Tw = 22.6°C

mc = 248 g

Cc = 0.386 J/g/°C

T = 39.9°C

Find: Tc

(390) (4.186) (39.9 - 22.6) = (248) (0.386) (Tc - 39.9)

Tc = 335

Answer 2

The initial temperature of the piece of copper is 335.6 °C.

Step 1:

Data obtained from the question

Mass of copper (M꜀) = 248 g

Volume of water  = 390 mL

Density of water = 1 g/mL

Initial temperature of water (Tᵥᵥ) = 22.6 °C

Equilibrium temperature (Tₑ) = 39.9 °C

Initial temperature of copper (T꜀) =?

Step 2:

Determination of the mass of water

Volume of water = 390 mL

Density of water = 1 g/mL

Mass of water =?

$Density = \frac{mass}{volume}\\\\1 = \frac{mass}{390}$

Cross multiply

$Mass = 1 * 390$

Mass of water = 390 g

Step 3:

Determination the initial temperature of the copper.

Mass of copper (M꜀) = 248 g

Mass of water (Mᵥᵥ) = 390 g

Initial temperature of water (Tᵥᵥ) = 22.6 °C

Equilibrium temperature (Tₑ) = 39.9 °C

Initial temperature of copper (T꜀) =?

NOTE:

1. Specific heat capacity of water (Cᵥᵥ) = 4.184 J/gºC

2. Specific heat capacity of copper (C꜀) = 0.385 J/gºC

Heat lost by copper = heat gained by water

$Q_{c} = Q_{w} \\ \ M_{c} C_{c}(T_{c}-T_{e}) = M_{w} C_{w}(T_{e}-T_{w})\\248* 0.385(T_{c}-39.9) = 390*4.184(39.9-22.6)\\95.48(T_{c}-39.9) = 1631.76*17.3\\95.48(T_{c}-39.9) = 28229.448$

Divide both side by 95.48

$T_{c} - 39.9 = \frac{28229.448}{95.48}\\T_{c} - 39.9 = 295.658$

Collect like terms

$T_{c} = 295.658 + 39.9$

T꜀ = 335.6 °C

Therefore, the initial temperature of the piece of copper is 335.6 °C.

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