In a calibration of a calorimeter, 50.0 g of water at 60.0 *C is added to 50.0 g of water at 20.0 *C to give a mixture at 39.0 *C. What is the heat capacity of the calorimeter used in this experiment? If the calorimeter has a mass of 5.4g, what is its specific heat?

To find the heat capacity of the calorimeter, we first need to calculate the heat absorbed or lost by the water.

The formula to calculate the heat absorbed or lost by a substance is:

Q = m * c * ΔT

Where:
Q = heat absorbed/lost
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature

In this case, we have two different masses of water (50.0 g and 50.0 g) at different initial temperatures (60.0 °C and 20.0 °C), resulting in a final temperature of 39.0 °C.

1. Calculate the heat absorbed by the hot water:

Q1 = m1 * c * ΔT1

m1 = 50.0 g (mass of hot water)
c = specific heat capacity of water (approximately 4.18 J/g°C)
ΔT1 = final temperature - initial temperature = 39.0 °C - 60.0 °C = -21.0 °C

Q1 = 50.0 g * 4.18 J/g°C * -21.0 °C

2. Calculate the heat lost by the cold water:

Q2 = m2 * c * ΔT2

m2 = 50.0 g (mass of cold water)
c = specific heat capacity of water (approximately 4.18 J/g°C)
ΔT2 = final temperature - initial temperature = 39.0 °C - 20.0 °C = 19.0 °C

Q2 = 50.0 g * 4.18 J/g°C * 19.0 °C

3. Calculate the total heat exchanged by summing the values of Q1 and Q2:

Q_total = Q1 + Q2

4. The total heat exchanged is equal to the heat absorbed or lost by the calorimeter, so we can write:

Q_total = m_calorimeter * c_calorimeter * ΔT_calorimeter

Given that the mass of the calorimeter is 5.4 g and the change in temperature is the same as the water, ΔT_calorimeter = -21.0 °C.

5. Rearrange the equation to solve for c_calorimeter:

c_calorimeter = Q_total / (m_calorimeter * ΔT_calorimeter)

Substitute the values of Q_total, m_calorimeter, and ΔT_calorimeter into the equation to find c_calorimeter.

Finally, to find the specific heat capacity of the calorimeter, divide the heat capacity (c_calorimeter) by the mass of the calorimeter:

specific heat of calorimeter = c_calorimeter / m_calorimeter