Question

consider the apparatus that joule used in his experiments on the mechanical equivalent of heat, shown in the figure below. suppose both blocks have a mass of 0.95 kg and that they fall consider the apparatus that joule used in his experiments on the mechanical equivalent of heat, shown below. suppose both blocks have a mass of 0.95 kg and that they fall through a distance of 0.48 m. find the expected rise in temperature of the water, given that 6200 j are needed for every 1.0°c increase. give your answer in celsius degrees. a. 3.3×10^(-4) °c b. 1.4×10^(-3) °c c. 7.1×10^(-6) °c d. 9.6×10^(-7) °c e. 5.4×10^(-5) °c

Explanation:

Step1: Calculate the work done by the blocks

The work - energy theorem is used. The work done by the two blocks is given by $W = 2mgh$, where $m = 0.95\ kg$, $g=9.8\ m/s^{2}$, and $h = 0.48\ m$.
$W=2\times0.95\times9.8\times0.48$
$W = 2\times0.95\times4.704=9.408\times0.95 = 8.9376\ J$

Step2: Calculate the temperature rise

We know that the heat required to raise the temperature of water is related to the work done. If $Q$ is the heat energy (equal to work done $W$ in this case) and $c$ is the heat - capacity factor ($6200\ J/^{\circ}C$), and $\Delta T$ is the temperature change, then $Q = c\Delta T$. So, $\Delta T=\frac{W}{c}$.
$\Delta T=\frac{8.9376}{6200}=1.44155\times 10^{-3}\ ^{\circ}C\approx1.4\times 10^{-3}\ ^{\circ}C$

Answer:

b. $1.4\times 10^{-3}\ ^{\circ}C$