A mass,m of water at 100degree celcius is added to another mass of water ,m at a temperature,t. The reslting temperature of the mixture is T. If the specific heat capacity of water is 4.2J/gk. Drive an expression for L terms of other quantities.
To derive an expression for L in terms of other quantities, we need to make use of the principle of conservation of energy.
The heat gained by the cooler water (m) is equal to the heat lost by the hotter water (m):
m * c * (T - t) = m * c * (100 - T)
Here's how we can break down this equation:
- m is the mass of both masses of water. Since both masses of water are equal, we only need to use one m.
- c is the specific heat capacity of water (4.2 J/gK), which is the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius.
- (T - t) is the temperature change of the cooler water. It started at a temperature t and ended up at temperature T.
- (100 - T) is the temperature change of the hotter water. It started at 100 degrees Celsius and ended up at temperature T.
Now, we can simplify the equation:
m * c * (T - t) = m * c * (100 - T)
Divide both sides of the equation by m and c:
(T - t) = (100 - T)
Now, let's solve for T:
T - t = 100 - T
Add T to both sides:
2T - t = 100
Add t to both sides:
2T = 100 + t
Divide both sides by 2:
T = (100 + t) / 2
Now, this is the expression for T in terms of t. To find the expression for L, we can substitute this expression for T back into our original equation:
L = m * c * (100 - T)
Substituting T:
L = m * c * (100 - (100 + t) / 2)
Simplifying further:
L = m * c * [(200 - (100 + t)) / 2]
L = m * c * (200 - 100 - t) / 2
L = m * c * (100 - t) / 2
Thus, the expression for L in terms of other quantities is:
L = m * c * (100 - t) / 2