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Chapter 8: Problem 1

Titanium is a metal used in jet engines. Its specific heat is \(0.523 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). If \(5.88 \mathrm{~g}\) of titanium absorbs \(4.78 \mathrm{~J}\), what is the change in temperature?

Short Answer

Expert verified
Answer: The change in temperature of the titanium is approximately 1.47°C.

Step by step solution

01

Write the given values.

We are given: Specific heat of titanium (c) = 0.523 J/g °C Mass of titanium (m) = 5.88 g Energy absorbed (q) = 4.78 J
02

Write the formula for calculating the change in temperature (ΔT).

The formula for calculating the change in temperature is: \(q = mcΔT\)
03

Rearrange the formula for ΔT.

We need to find ΔT, so we will rearrange the formula: \(ΔT = \frac{q}{mc}\)
04

Plug in the given values and calculate ΔT.

Now we will substitute the given values for q, m, and c in the formula: \(ΔT = \frac{4.78 \mathrm{~J}}{5.88 \mathrm{~g} \times 0.523 \mathrm{~J / g\cdot ^{\circ}C}}\)
05

Solve for ΔT.

Now, calculate the value of ΔT: \(ΔT = \frac{4.78 \mathrm{~J}}{ (5.88 \mathrm{~g}) \times (0.523 \mathrm{~J / g\cdot ^{\circ}C})} \approx 1.47^{\circ} C\) The change in temperature of the titanium is approximately 1.47°C.

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Most popular questions from this chapter

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