Hot water at a temperature of t is added to twice the amount of water at the temperature of 30 degrees C.if the resulting temperature of the mixture is 50 degrees C.calculate t

To find the temperature \( t \) of the hot water, we can use the principle of conservation of energy. The heat lost by the hot water must equal the heat gained by the cooler water.

Let:
- \( m \) be the mass of the hot water (with temperature \( t \)).
- \( 2m \) be the mass of the cooler water (with temperature \( 30^\circ C \)).
- \( T_f \) be the final temperature of the mixture, which is \( 50^\circ C \).

Using the formula for heat transfer, we have:

\[
\text{Heat lost by hot water} = \text{Heat gained by cooler water}
\]

This can be expressed as:

\[
m c (t - T_f) = 2m c (T_f - 30)
\]

Where \( c \) is the specific heat capacity of water. Since \( c \) and \( m \) are common to both sides, they can be canceled out:

\[
t - 50 = 2(50 - 30)
\]

Calculating the right-hand side:

\[
t - 50 = 2 \times 20 = 40
\]

Now, solving for \( t \):

\[
t = 50 + 40 = 90
\]

Thus, the temperature \( t \) of the hot water is **90 degrees Celsius**.

If you want further details or have any questions, let me know! Here are some related questions you might consider:

1. What assumptions are made in this calculation?
2. How would the result change if the final temperature were different?
3. What is the effect of using a different amount of cooler water?
4. How does the specific heat capacity of water influence the result?
5. Can this principle be applied to other substances besides water? 

**Tip:** Always ensure to account for the masses and temperatures of all substances involved when using conservation of energy principles!

Hot water at a temperature of t is added to twice the amount of water at the temperature of 30 degrees C. If the resulting temperature of the mixture is 50 degrees C, calculate t.

Discover how to calculate the temperature of hot water in a mixing problem where hot water at temperature t is combined with cooler water at 30 degrees C, resulting in a final temperature of 50 degrees C. This problem illustrates key concepts of heat transfer and energy conservation.

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