## You Are At A Restaurant Eating Lunch With A Friend.

Specific heat, denoted Cp, is a calculation that measures the amount of heat needed to raise the temperature of a substance by one degree Celsius. It is calculated using the equation Cp = Q/mΔT, where m is the mass of the substance and ΔT is the change in temperature. This formula can be manipulated to find the change in heat rather than specific heat. The specific heat capacity is measured in joules per Kelvin per kilogram (J⋅kg−1⋅K−1) and can be used to calculate the heat required to raise the temperature of a given substance, like water. This concept is explained in a chemistry video and illustrated in an example where the specific heat is 129 J/kg⋅K and the temperature is 50.0 K.

The specific heat of a substance can be calculated using the formula:

C = Q / (m * ΔT),

where C is the specific heat, Q is the heat added, m is the mass of the substance, and ΔT is the change in temperature.

In this case, we need to determine the specific heat of the metal given to you by your friend, which we'll denote as C_metal. We have the specific heat of silver (C_silver) and the specific heat of lead (C_lead), which are 235 J/(kg*°C) and 130 J/(kg*°C), respectively.

Using the conservation of energy, we can set up the equation:

m_metal * C_metal * ΔT + m_lead * C_lead * ΔT = 0

where m_metal is the mass of the metal, m_lead is the mass of the lead container, and ΔT is the change in temperature.

We were also given the masses and initial and final temperatures of the water and the entire "silver"-lead-water system.

By using the given information, the specific heat of the metal can be calculated using the conservation of energy equation. Using the mass and temperature values provided, we can solve for C_metal. This will allow you to evaluate whether the metal is actually pure silver or not, and make your decision about remaining friends based on the given specific heat values.

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