A 37.0 g mass of a metal was heated to 100°C and then plunged into 74 g of water at 24.0°C. The temperature of the resulting mixture became 28.0°C.

(a) How many joules did the water absorb?
(b) How many joules did the metal lose?
(c) What is the heat capacity of the metal sample?
(d) What is the specific heat of the metal?

a.

joules H2O absorbed = mass H2O x spcific heat H2O x (Tfinal-Tinitial)

b.
joules absorbed by H2O = heat gained by metal

d.
q metal = mass metal x specific heat metal x (Tfinal-Tinitial)

c. q = mass metal x delta T

To solve this problem, we can use the formula for heat transfer:

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.

(a) To find the heat absorbed by the water, we can use the formula as follows:

Q_water = mcΔT

Given:
m_water = 74 g and ΔT_water = 28.0 - 24.0 = 4.0°C

Since the specific heat of water is approximately 4.18 J/g°C, we can substitute the values into the formula:

Q_water = (74 g) * (4.18 J/g°C) * (4.0°C)
Q_water = 1235.52 J

Therefore, the water absorbed 1235.52 joules of heat.

(b) To find the heat lost by the metal, we can use the formula as follows:

Q_metal = mcΔT

Given:
m_metal = 37.0 g and ΔT_metal = 100 - 28.0 = 72°C

Since we don't know the specific heat capacity of the metal, we'll label it c_metal for now.

Q_metal = (37.0 g) * (c_metal) * (72°C)

(c) To find the heat capacity of the metal sample, we need to know the heat lost by the metal (which we found in part (b)) and the change in temperature. The heat capacity is given by:

C_metal = Q_metal / ΔT_metal

Substituting the values:

C_metal = Q_metal / ΔT_metal = (37.0 g) * (c_metal) * (72°C) / (72°C)

(d) Lastly, to find the specific heat of the metal, we can rearrange the formula for heat capacity:

c_metal = C_metal / m_metal

Substituting the values:

c_metal = C_metal / m_metal = (37.0 g) * (c_metal) * (72°C) / (72°C) / (37.0 g)

Please note that in order to complete parts (c) and (d), we need additional information about the heat capacity or specific heat of the metal.

To answer these questions, we can use the principle of heat transfer, which states that the heat gained by one object is equal to the heat lost by another object in a closed system. We'll need to use the equation:

Q = m * c * ΔT

Where Q is the heat transfer, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature.

(a) To determine how many joules the water absorbed, we'll use the equation Q = m * c * ΔT.

The mass of the water is 74 g, the specific heat capacity of water is 4.18 J/g°C (or 4.18 J/gK), and the change in temperature is (28.0 - 24.0) = 4.0°C.

Q = 74 g * 4.18 J/g°C * 4.0°C
Q = 1234.64 J

Therefore, the water absorbed approximately 1235 J of heat.

(b) To determine how many joules the metal lost, we'll again use the equation Q = m * c * ΔT.

The mass of the metal is 37.0 g, and the change in temperature is (100.0 - 28.0) = 72.0°C (or 72.0 K).

Q = 37.0 g * c * 72.0°C
Q = 37.0 g * c * 72.0 K

To calculate the exact value of Q, we would need to know the specific heat capacity of the metal, which is not provided in the question. We'll need to use additional information or assume a specific heat capacity for the metal.

(c) The heat capacity of an object is the amount of heat energy required to raise its temperature by 1°C (or 1K). It is calculated using the equation C = m * c.

Since we don't know the specific heat capacity of the metal, we can't calculate the exact heat capacity of the metal sample without additional information.

(d) The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of one gram of that substance by 1°C (or 1K). It is calculated using the equation c = Q / (m * ΔT).

Similarly, since we don't know the exact heat transfer for the metal without knowing its specific heat capacity, we can't calculate the specific heat of the metal either.

In summary, we can determine how much heat energy the water absorbed but need additional information to calculate the heat loss or specific heat capacity of the metal sample.