Question

A piece of metal with a mass of 1.9 kg, specific heat of 243 j/kg/°c, and initial temperature of 83°c is dropped into an insulated jar that contains liquid with a mass of 4 kg, specific heat of 1000 j/kg/°c, and initial temperature of 0°c. the piece of metal is removed after 5.1 s, at which time its temperature is 23°c. find the temperature of the liquid after the metal is removed. neglect any effects of heat transfer to the air or to the insulated jar.

Answer 1

To find the final temperature of the liquid, use the conservation of energy principle via the calorimetry equation. Calculate the heat lost by the metal with the formula Q = mcΔT and set it equal to the heat gained by the liquid, then solve for the final temperature of the liquid after the metal is removed.

Step-by-step explanation:

To calculate the temperature of the liquid after the metal is removed, we can use the principle of conservation of energy, which in this context is often referred to as the calorimetry equation. This equation asserts that the heat lost by the metal will be equal to the heat gained by the liquid, as there is no heat transfer to the surrounding environment.

For the metal, the heat lost can be calculated using the formula: Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Plugging in the values for the metal (m=1.9 kg, c=243 J/kg/°C, initial T=83°C, final T=23°C), we get a heat loss for the metal.

For the liquid, the heat gained will be the same as the heat lost by the metal. Assuming the final temperature of the liquid after 5.1 seconds to be T_f, the heat gained by the liquid would be Q = 4 kg * 1000 J/kg/°C * (T_f - initial T of liquid).

Since the heat lost by the metal equals the heat gained by the liquid, we can set the two equations equal to each other and solve for T_f, which would give us the final temperature of the liquid.

Answer 2

The final temperature of the liquid after the metal is removed if the piece of metal is removed after 5.1 s, at which time its temperature is 23°c is approximately -5.06°C.

Step-by-step explanation:

To find the temperature of the liquid after the metal is removed, we can use the principle of conservation of energy. The heat lost by the metal will be equal to the heat gained by the liquid. The heat lost by the metal can be calculated using the formula:
Q = mcΔT

Where Q is the heat lost, m is the mass, c is the specific heat, and ΔT is the change in temperature.

Using the given values, we have:

Qmetal = 1.9 kg * 243 J/kg/°C * (23°C - 83°C) = -20253 J

The negative sign indicates that the metal is losing heat. Since the heat lost by the metal is equal to the heat gained by the liquid, we can calculate the final temperature of the liquid using the formula:

Qliquid = m * c * ΔT

Considering the heat gained by the liquid, we have:

-20253 J = 4 kg * 1000 J/kg/°C * (T - 0°C)

-20253 J = 4000 J/°C * T

Dividing both sides of the equation by 4000 J/°C, we find:

-5.06325 = T

Therefore, the final temperature of the liquid is approximately -5.06°C.