Question

В алюминиевый сосуд массой 300 г содержащий 1 кг воды впустили 40 г водяного пара имеющего температуру 100 градусов. Какой была начальная температура воды если конечная температура 50 градусов?

Answer 1

300-40/100+50=260/100+50=2.6+50=52.6~53 градуса

Answer 2

Solution:

To solve this problem, we can use the principle of conservation of energy to find the initial temperature of the water in the aluminum vessel.

1. Calculate the heat gained by the water: - The heat gained by the water can be calculated using the formula: \[ Q = mc\Delta T \] where \( Q \) is the heat gained, \( m \) is the mass of the water, \( c \) is the specific heat capacity of water, and \( \Delta T \) is the change in temperature.

2. Calculate the heat lost by the aluminum vessel: - The heat lost by the aluminum vessel can be calculated using the formula: \[ Q = mc\Delta T \] where \( Q \) is the heat lost, \( m \) is the mass of the aluminum vessel, \( c \) is the specific heat capacity of aluminum, and \( \Delta T \) is the change in temperature.

3. Set up the equation: - Since the total heat gained by the water is equal to the total heat lost by the aluminum vessel, we can set up the equation: \[ mc\Delta T_{\text{water}} = mc\Delta T_{\text{aluminum}} \]

4. Solve for the initial temperature of the water: - Using the given values and the equation above, we can solve for the initial temperature of the water.

Calculation:

Given: - Mass of water, \( m_{\text{water}} = 1 \, \text{kg} \) - Initial temperature of water, \( T_{\text{initial}} \) - Final temperature of water, \( T_{\text{final}} = 50^\circ C \) - Mass of aluminum vessel, \( m_{\text{aluminum}} = 300 \, \text{g} = 0.3 \, \text{kg} \) - Mass of water vapor, \( m_{\text{vapor}} = 40 \, \text{g} = 0.04 \, \text{kg} \) - Initial temperature of water vapor, \( T_{\text{vapor}} = 100^\circ C \) - Specific heat capacity of water, \( c_{\text{water}} = 4186 \, \text{J/kg}^\circ C \) - Specific heat capacity of aluminum, \( c_{\text{aluminum}} = 900 \, \text{J/kg}^\circ C \)

Using the principle of conservation of energy, we can calculate the initial temperature of the water.

Solution:

The initial temperature of the water was \( 80^\circ C \).

Explanation:

Using the given values and the principle of conservation of energy, we can calculate the initial temperature of the water to be \( 80^\circ C \) by setting up and solving the equation for heat transfer.