Question

a 119 g metal bar requires 2.50 kj to change its temperature from 27.5 °c to 100.0 °c. what is the specific heat of the metal? j/g°c

Explanation:

Step1: Convert energy to joules

$2.50\ kJ = 2.50\times10^{3}\ J$

Step2: Calculate temperature change

$\Delta T=100.0^{\circ}C - 27.5^{\circ}C=72.5^{\circ}C$

Step3: Use specific - heat formula

The formula for heat is $Q = mc\Delta T$, where $Q$ is heat, $m$ is mass, $c$ is specific heat, and $\Delta T$ is temperature change. Rearranging for $c$ gives $c=\frac{Q}{m\Delta T}$. Substitute $Q = 2.50\times 10^{3}\ J$, $m = 119\ g$, and $\Delta T=72.5^{\circ}C$ into the formula: $c=\frac{2.50\times 10^{3}\ J}{119\ g\times72.5^{\circ}C}$

Step4: Calculate specific heat

$c=\frac{2.50\times 10^{3}}{119\times72.5}\ J/g^{\circ}C=\frac{2500}{8627.5}\ J/g^{\circ}C\approx0.290\ J/g^{\circ}C$

Answer:

$0.290$