Question

The specific heat of ethylene glycol is \(2.42 \mathrm{~J} / \mathrm{g}-\mathrm{K} .\) How many J of heat are needed to raise the temperature of \(62.0 \mathrm{~g}\) of ethylene glycol from \(13.1^{\circ} \mathrm{C}\) to \(40.5^{\circ} \mathrm{C}\) ?

Short answer

Approximately \(4188.5 \mathrm{~J}\) of heat are needed to raise the temperature of \(62.0 \mathrm{~g}\) of ethylene glycol from \(13.1^{\circ} \mathrm{C}\) to \(40.5^{\circ} \mathrm{C}\).

Step-by-step solution

Identify the given values

We have been given the following values: - Specific Heat (c) = 2.42 J/g-K - Mass (m) = 62.0 g - Initial Temperature (T1) = 13.1°C - Final Temperature (T2) = 40.5°C

Calculate the temperature change

We need to find the temperature change (∆T), so we subtract the initial temperature (T1) from the final temperature (T2): ∆T = T2 - T1 ∆T = 40.5°C - 13.1°C ∆T = 27.4 K

Use the formula to calculate the heat required

Now that we have all the values, we can use the formula: Heat (Q) = Mass (m) x Specific Heat (c) x Temperature Change (∆T) Q = (62.0 g) x (2.42 J/g-K) x (27.4 K)

Calculate the heat required

Multiply the values to get the result: Q = 62.0 x 2.42 x 27.4 Q ≈ 4188.5 J So, approximately 4188.5 J of heat are needed to raise the temperature of 62.0 g of ethylene glycol from 13.1°C to 40.5°C.