Question

calculate the amount of heat needed, in kj, to heat 7.8 g of water from 8.31°c to 48.35°c. note that the specific heat of water is 4.184 j/g°c.
report your answer to 2 places past the decimal point.

Explanation:

Step1: Calculate the temperature change

The formula for temperature change $\Delta T=T_{final}-T_{initial}$.
Given $T_{initial} = 8.31^{\circ}C$ and $T_{final}=48.35^{\circ}C$, so $\Delta T=48.35 - 8.31=40.04^{\circ}C$.

Step2: Use the heat - formula

The heat formula is $Q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the temperature change.
Given $m = 7.8g$, $c=4.184J/g^{\circ}C$, and $\Delta T = 40.04^{\circ}C$.
Substitute the values into the formula: $Q=7.8\times4.184\times40.04$.
First, calculate $7.8\times4.184 = 32.6352$.
Then, $32.6352\times40.04=32.6352\times(40 + 0.04)=32.6352\times40+32.6352\times0.04=1305.408+1.305408 = 1306.713408J$.

Step3: Convert joules to kilojoules

Since $1kJ = 1000J$, then $Q=\frac{1306.713408}{1000}=1.306713408kJ$.

Answer:

$1.31kJ$