how to determine the amount of water in the container when you are given a 200g piece of aluminium at 90 degrees celcius is placed in a 100g glass container which holds an unknown amount of water at 20 degrees celcius .if the equilibrium temperature is 21.6 degrees celsius(refer to tables for the needy specific heat capacities)
To determine the amount of water in the container, we can use the principle of energy conservation.
First, we need to calculate the energy gained by the water and the energy lost by the aluminum until they reach the equilibrium temperature.
The equation for energy gained or lost (Q) can be calculated using the formula:
Q = mcΔT
Where:
Q is the energy gained or lost (in Joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g·°C)
ΔT is the change in temperature (in °C)
Let's break down the steps to solve this problem:
1. Calculate the energy lost by the aluminum:
- Mass of aluminum (m1) = 200g
- Initial temperature of aluminum (T1) = 90°C
- Final temperature of aluminum and water (Tf) = 21.6°C
- Specific heat capacity of aluminum (c1) is given in the table (in J/g·°C)
- Energy lost by the aluminum (Q1) = m1 * c1 * (T1 - Tf)
2. Calculate the energy gained by the water:
- Mass of water (m2) = unknown
- Initial temperature of water (T2) = 20°C
- Final temperature of aluminum and water (Tf) = 21.6°C
- Specific heat capacity of water (c2) is given in the table (in J/g·°C)
- Energy gained by the water (Q2) = m2 * c2 * (Tf - T2)
3. Since the energy lost by the aluminum is equal to the energy gained by the water, we can set up the equation:
Q1 = Q2
4. Solve the equation to find the mass of water in the container:
m2 = (m1 * c1 * (T1 - Tf)) / (c2 * (Tf - T2))
By plugging in the provided values and the specific heat capacities for aluminum and water, you can calculate the mass of the water in the container.
To determine the amount of water in the container, we need to use the concept of heat transfer and the specific heat capacities of the materials involved. Here's a step-by-step approach to solve the problem:
Step 1: Determine the heat gained by water.
- The heat gained by the water can be calculated using the formula: Q = m * c * ΔT, where Q is the heat gained, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.
- The mass of water is unknown, so let's call it "m_w".
- The specific heat capacity of water can be found from tables, and it is approximately 4.18 J/g°C.
- The change in temperature is given as 21.6°C - 20°C = 1.6°C.
- Therefore, the heat gained by the water can be calculated as Q_w = m_w * 4.18 J/g°C * 1.6°C.
Step 2: Determine the heat lost by the aluminum.
- The heat lost by the aluminum can also be calculated using the formula: Q = m * c * ΔT.
- The mass of aluminum is given as 200g.
- The specific heat capacity of aluminum can be found from tables, and it is approximately 0.897 J/g°C (for temperatures above 0°C).
- The change in temperature is the final temperature of the system (21.6°C) minus the initial temperature of the aluminum (90°C).
- Therefore, the heat lost by the aluminum can be calculated as Q_aluminum = 200g * 0.897 J/g°C * (21.6°C - 90°C).
Step 3: Equate the heat gained by water to the heat lost by aluminum.
- Since the heat gained by the water is equal to the heat lost by the aluminum (Q_w = Q_aluminum), we can set up the equation:
m_w * 4.18 J/g°C * 1.6°C = 200g * 0.897 J/g°C * (21.6°C - 90°C)
- Simplify the equation and solve for m_w:
m_w = (200g * 0.897 J/g°C * (21.6°C - 90°C)) / (4.18 J/g°C * 1.6°C)
- Calculate the value of m_w to determine the mass of water in the container.
Step 4: Calculate the volume of water in the container.
- Use the mass of water (m_w) and the density of water (approximately 1 g/mL or 1 g/cm³) to calculate the volume of water in the container.
- Volume = mass / density.
Following these steps will help you determine the amount of water in the container.