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Chapter 2: Problem 142

The specific heat of methane gas is \(2.20 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). If the temperature of a sample of methane gas rises by \(15^{\circ} \mathrm{C}\) when \(8.8 \mathrm{~kJ}\) of heat energy is added to the sample, what is the mass of the sample?

Short Answer

Expert verified
The mass of the methane gas sample is approximately \(266.67 \textrm{ grams}\) when 8.8 kJ of heat energy is added, and the temperature rises by \(15^{\circ} \mathrm{C}\).

Step by step solution

01

Convert given units

First, let's convert the given units to the standard units. The heat energy Q is given as 8.8 kJ, which needs to be converted to J (joules). 1 kJ = 1000 J So, 8.8 kJ = 8.8 × 1000 J = 8800 J
02

Identify the given values

Now, let's identify the given values: Specific heat (c) = 2.20 J/g°C Temperature change (ΔT) = 15°C Heat energy (Q) = 8800 J
03

Use the formula Q = mcΔT

Now we can use the formula for heat transfer to find the mass of the sample: Q = mcΔT Rearrange the formula to solve for the mass (m): m = Q / (cΔT)
04

Plug in the given values and solve for mass

Now, plug in the given values to calculate the mass: m = (8800 J) / (2.20 J/g°C × 15°C) m = (8800 J) / (33 J/g) m ≈ 266.67 g
05

State the result

The mass of the methane gas sample is approximately 266.67 grams.

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