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  • An experiment is conducted to determine the specific heat capacity (c) of a metal using the method of mixtures. A known mass of the metal at a temperature T1 = 100°C is placed in a c

An experiment is conducted to determine the specific heat capacity (c) of a metal using the method of mixtures. A known mass of the metal at a temperature T1 = 100°C is placed in a calorimeter containing a known mass of water at a lower temperature T2 = 20°C. The final equilibrium temperature Tf is observed to be 30°C. Given that the mass of the metal is m1 = 0.2 kg and the mass of water is m2 = 0.5 kg, calculate the specific heat capacity of the metal.

Option: 1

150 J/kg°C


Option: 2

2500 J/kg°C


Option: 3

1100 J/kg°C


Option: 4

1500 J/kg°C


Answers (1)

best_answer

Given values:

Initial temperature of the metal (T1) = 100°C
Initial temperature of water (T2) = 20°C
Final equilibrium temperature (Tf ) = 30°C
Mass of the metal (m1) = 0.2 kg
Mass of water (m2) = 0.5 kg

The heat gained by the metal (Q1) is equal to the heat lost by the water (Q2):

                    Q1 = Q2

The heat gained by the metal can be calculated using the formula:

                    Q_{1} = m_{1} . c . \Delta T_{1}

The heat lost by the water can be calculated using the formula:

                    Q_{2} = m_{2} . c_{water} . \Delta T_{2}

where cwater is the specific heat capacity of water.

Since Q1 = Q2, we have:

                    m_{1} . c . \Delta T_{1} = m_{2} . c_{water} . \Delta T_{2}

Solve for c:

                    c = \frac{m_{2} . c_{water} . \Delta T_{2}}{m_{1} . \Delta T_{1} }

Step 1:

Calculate the temperature differences:

                    \Delta T_{1} = |T_{f} - T_{1} = 30 \degree C - 100 \degree C| = 70 \degree C

\Delta T_{2} = T_{f} - T_{2} = 30 \degree C - 20 \degree C = 10 \degree C

Step 2: Calculate the specific heat capacity of water:

                    cwater = 4200 J/kg°C

Step 3: Substitute the values and calculate c:

c = \frac{0.5 kg . 4200 J/kg\degree C . 10\degree C}{0.2 kg . (70)\degree C}

Step 4: Calculate c:

                    c = 1500 J/kg°C

The specific heat capacity of the metal is calculated to be 1500 J/kg°C.

Posted by

Kuldeep Maurya

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