Equal 0.400-kg masses of lead and tin at 60.0°C are placed in 1.00 kg of water at 20.0°C. If an alloy is half lead and half tin by mass, what specific heat would you anticipate for the alloy?

Answer 1

To solve this problem, we can use the principle of energy conservation.

First, let's calculate the total energy gained by the water. We can use the equation:

Q_water = m_water * c_water * ΔT

where:
- Q_water is the energy gained by the water
- m_water is the mass of the water (1.00 kg)
- c_water is the specific heat of water (4.18 J/g°C)
- ΔT is the change in temperature of the water (final temperature - initial temperature)

ΔT = final temperature - initial temperature
= Tf - Ti
= 60.0°C - 20.0°C
= 40.0°C

Q_water = (1.00 kg) * (4.18 J/g°C) * (40.0°C)
= 167.2 J

Next, let's calculate the total energy lost by the lead and tin. Since both masses are equal and half of the alloy, we can calculate the energy lost by one of the metals and then multiply it by 2.

Q_lead or tin = m_lead or tin * c_lead or tin * ΔT

where:
- Q_lead or tin is the energy lost by lead or tin
- m_lead or tin is the mass of lead or tin (0.400 kg)
- c_lead or tin is the specific heat of lead or tin (to be determined)
- ΔT is the change in temperature of lead or tin (final temperature - initial temperature)

Q_lead or tin = (0.400 kg) * c_lead or tin * ΔT

Since the alloy is half lead and half tin by mass, the total energy lost by lead and tin is:

Q_total = (Q_lead or tin) + (Q_lead or tin)
= 2 * (0.400 kg) * c_lead or tin * ΔT
= 0.800 kg * c_lead or tin * ΔT

Finally, using the principle of energy conservation, the energy gained by the water is equal to the total energy lost by the lead and tin:

Q_water = Q_total

167.2 J = 0.800 kg * c_lead or tin * ΔT

Substituting the value of ΔT:

167.2 J = 0.800 kg * c_lead or tin * 40.0°C

Simplifying the equation:

167.2 J = 32.0 kg°C * c_lead or tin

Dividing both sides by 32.0 kg°C:

c_lead or tin = 167.2 J / 32.0 kg°C
c_lead or tin = 5.225 J/g°C

Therefore, the specific heat anticipated for the alloy is 5.225 J/g°C.