If temperature t is directly proportional to heat h, and when t = 20oC, h = 50 J, find t when h = 60J

Analysis

The question states that temperature ($t$) is directly proportional to heat ($h$). This means that as one increases, the other increases at a constant rate. Mathematically, this is expressed as $t \propto h$, which converts to the equation $t = kh$, where $k$ is the constant of proportionality.

Concept

To solve this, we follow two steps:

1. Find the constant ($k$): Use the initial values provided ($t = 20$ and $h = 50$) to determine the value of $k$.
2. Solve for the unknown: Use the value of $k$ and the new value of $h$ ($60$) to calculate the new temperature ($t$).

Step-by-Step Solution

Step 1: Find $k$ Given: $t = 20$, $h = 50$ Using the formula $t = kh$: $20 = k \times 50$ $k = \frac{20}{50}$ $k = 0.4$

Step 2: Find $t$ when $h = 60$ Using the formula $t = kh$ with our known $k$: $t = 0.4 \times 60$ $t = 24$

The temperature is $24^\circ\text{C}$.

Conclusion

Comparing our result to the given options, the correct answer is A.

Exam Tip

When dealing with direct proportion questions like this, you can also use the ratio method:

Substituting the values:

This method is often faster and helps you avoid errors when calculating the constant $k$ separately!