As a physicist, you put heat into a $500 g$ solid sample at the rate of $10.0 k J / m i n$ , while recording its temperature as a function of time. You plot your data and obtain the graph shown in figure. What is the specific heat of solid state of the material?

2.66 k J / k g^{\circ} C

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4.99 k J / k g^{\circ} C

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1.33 k J / k g^{\circ} C

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None of these

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Solution

The correct option is C $1.33 k J / k g^{\circ} C$
Specific heat of solid state is the amount of heat required to raise the temperature of 1gram of solid by $1^{\circ} C$
The initial portion (straight line) corresponds to heating of the solid.
From figure, $Δ T = (10 - (- 5)) = 15^{\circ} C$ ,
Heat consumed $Δ Q = (10 k J / m i n \times 1 m i n) = 10 k J$
Specific heat $C = \frac{1}{m} \frac{d Q}{d T} = \frac{1}{0.5} \frac{10}{15} = 1.33 k J / (k g^{\circ} C)$
Hence, Option C is correct.

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As a physicist, you put heat into a 500 g solid sample at the rate of 10.0 kJ/min, while recording its temperature as a function of time. You plot your data and obtain the graph shown in figure. What is the specific heat of solid state of the material?

As a physicist, you put heat into a $500 g$ solid sample at the rate of $10.0 k J / m i n$ , while recording its temperature as a function of time. You plot your data and obtain the graph shown in figure. What is the specific heat of solid state of the material?