Question

You fill a cup with 0.200 kg of water at 100°C and then add ice to lower the temperature to 65°C after equilibrium is reached. What mass of ice do you need to add? The ice is initially at 0°C, the temperature at which it melts. The specific heat capacity of water is 4.18 × 103 J/(kg ∙ K) and the specific transformation energy for melting ice is 334 × 103 J/kg. A. 0.048 kg B. 0.088 kg C. 0.11 kg D. 0.37 kg E. 0.47kg 15) (8 pts.) An ideal gas is in a chamber with a plunger on top. While a constant force is applied to the plunger the chamber is heated by a flame. Which of the following statements are correct? A. = ∆ B. = −B∆ C. ∆th = ∆ D. A and C E. All of the above.

Answer 1

To determine the specific heat capacity of the metal, we apply the conservation of energy, equate the heat lost by the metal to the heat gained by the water, and solve for the specific heat capacity using the given masses, temperatures, and the specific heat capacity of water.

Step-by-step explanation:

To calculate the specific heat capacity of the metal, we assume that no heat is lost to the surroundings and that the heat lost by the metal is equal to the heat gained by the water until thermal equilibrium is reached. The formula for heat transfer Q is Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Applying the principle of conservation of energy, we set the heat lost by the metal equal to the heat gained by the water.

For the hot metal, Q_metal = m_metal * c_metal * (ΔT_metal), and for water, Q_water = m_water * c_water * (ΔT_water). We know the following: m_metal = 0.0345 kg, m_water = 0.064 kg, c_water = 4180 J/(kg·K), initial temperature of metal T_metal_initial = 75°C, initial temperature of water T_water_initial = 25°C, and final equilibrium temperature T_final = 39°C.

We can calculate the heat transfer for the water (Q_water) as follows:
Q_water = m_water * c_water * (T_final - T_water_initial) = 0.064 kg * 4180 J/(kg·K) * (39°C - 25°C).

Then the heat transfer for the metal (Q_metal) is:
Q_metal = Q_water
0.0345 kg * c_metal * (75°C - 39°C) = Q_water.

By solving for c_metal, we get the specific heat capacity of the metal: