Question

The specific heat of plastic is 50 times greater than the specific heat of lead, 10 times greater than the specific heat of stone, and 1.5 times greater than the specific heat of water. If the samples of plastic, lead, stone, and water have identical masses and identical starting temperatures, and are given identical increases in energy of 1,000 J, which sample will end up with the highest temperature?

A. plastic
B. lead
C. stone
D. water
E. None of the Above

Answer 1

Question #78236, Chemistry / General Chemistry

The specific heat of plastic is 50 times greater than the specific heat of lead, 10 times greater than the specific heat of stone, and 1.5 times greater than the specific heat of water. If the samples of plastic, lead, stone, and water have identical masses and identical starting temperatures, and are given identical increases in energy of 1,000 J, which sample will end up with the highest temperature?

A. plastic

B. lead

C. stone

D. water

E. None of the Above

SOLUTION

$$Q = c * m * \Delta t,$$

in it Q is the heat energy, J;

$c_1$ is the specific heat of plastic $J/(g^{+*}C)$;

$c_2$ is the specific heat of lead $J/(g^+ \text{lead}^*C)$;

$c_3$ is the specific heat of stone $J/(g^{+*}C)$;

$c_4$ is the specific heat of water $J/(g^{+*}C)$;

m is the mass of the substance, g;

$\Delta t_1$ is the change temperature of plastic in $^\circ \mathrm{C}$;

$\Delta t_2$ is the change temperature of lead in $^\circ \mathrm{C}$;

$\Delta t_3$ is the change temperature of stone in $^\circ \mathrm{C}$;

$\Delta t_4$ is the change temperature of water in $^\circ \mathrm{C}$;

$$\begin{array}{l} \Delta t_1 = Q / (c_1 * m), \\ \Delta t_2 = Q / (c_2 * m), \\ \Delta t_3 = Q / (c_3 * m), \\ \Delta t_4 = Q / (c_4 * m), \end{array}$$ $$\Delta t_1: \Delta t_2: \Delta t_3: \Delta t_4 = \frac{1,000}{c_1 * m}: \frac{50 * 1,000}{c_1 * m}: \frac{10 * 1,000}{c_1 * m}: \frac{1.5 * 1,000}{c_1 * m} = 1:50:10:1.5,$$ $$\Delta t_2 > \Delta t_3 > \Delta t_4 > \Delta t_1$$

the change temperature of lead is 50 times greater of plastic;

the change temperature of stone is 10 times greater of plastic;

the change temperature of water is 1.5 times greater of plastic.

$$\begin{array}{l} \Delta t = t_{\text{end}} - t_{\text{start}} \\ t_{\text{end}} = t_{\text{start}} + \Delta t, \\ t_{\text{start1}} = t_{\text{start2}} = t_{\text{start3}} = t_{\text{start4}} \\ \end{array}$$

then $t_{2\text{end}} > t_{3\text{end}} > t_{4\text{end}} > t_{1\text{end}}$

ANSWER:B.

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