complete combustion of a 0.600 - g sample of a compound in a bomb calorimeter releases 24.0 kj of heat. the…
complete combustion of a 0.600 - g sample of a compound in a bomb calorimeter releases 24.0 kj of heat. the bomb calorimeter has a mass of 1.30 kg and a specific heat of 3.41 j/(g·°c). if the initial temperature of the calorimeter is 25.5°c, what is its final temperature? use q = mc_pδt.\n30.9°c\n34.5°c\n44.0°c\n51.5°c
Answer
Explanation:
Step1: Convert mass unit and heat unit
First, convert the mass of the calorimeter to grams ($m = 1.30\ kg=1300\ g$) and the heat released to joules ($q = 24.0\ kJ = 24000\ J$).
Step2: Rearrange the heat - capacity formula
The formula is $q = mc_p\Delta T$, and we want to find $\Delta T$. Rearranging gives $\Delta T=\frac{q}{mc_p}$. Substitute $q = 24000\ J$, $m = 1300\ g$, and $c_p=3.41\ J/(g^{\circ}C)$ into the formula: $\Delta T=\frac{24000}{1300\times3.41}\approx5.4^{\circ}C$.
Step3: Calculate the final temperature
We know that $\Delta T=T_f - T_i$. So, $T_f=\Delta T+T_i$. Given $T_i = 25.5^{\circ}C$ and $\Delta T\approx5.4^{\circ}C$, then $T_f=25.5 + 5.4=30.9^{\circ}C$.
Answer:
$30.9^{\circ}C$