A mass of water m at 💯 degree Celsius is added to another Mass of water m at a temperature t.the resulting temperature of the mixture is t if the specific heat capacity of water is 4200 derive an expression t in terms of other questions
To derive an expression for the resulting temperature, t, of the mixture, we can use the principle of conservation of energy. The energy lost by the hot water is equal to the energy gained by the cold water.
Let's denote the mass of the hot water as m1, its initial temperature as 100°C, and the mass of the cold water as m2, with an initial temperature of t.
The energy lost by the hot water can be calculated using the formula:
Energy lost by hot water = mass of hot water (m1) * specific heat capacity of water * change in temperature
The energy gained by the cold water can be calculated using the formula:
Energy gained by cold water = mass of cold water (m2) * specific heat capacity of water * change in temperature
Since the total energy lost by the hot water is equal to the energy gained by the cold water, we can set the two formulas equal to each other:
m1 * 4200 * (100 - t) = m2 * 4200 * (t - t)
We can simplify this equation:
m1 * (100 - t) = m2 * t
Next, let's rearrange the equation to solve for the resulting temperature, t:
m1 * 100 - m1 * t = m2 * t
m1 * 100 = m1 * t + m2 * t
We can factor out t from the right-hand side of the equation:
m1 * 100 = (m1 + m2) * t
Dividing both sides by (m1 + m2):
t = (m1 * 100) / (m1 + m2)
So, the expression for the resulting temperature, t, of the mixture is:
t = (m1 * 100) / (m1 + m2)