Question

Calculate the difference between the heat of combustion of $CO$ at constant pressure and at constant volume at ${27^\circ }C$ ?
$R = 2cal{K^{ - 1}}mo{l^{ - 1}}$
A. $54$
B. $600$
C. $ - 300$
D. $27cal$

Answer 1

Hint: The heats of combustion of $CO$ at constant pressure and at constant volume at differs. This can be attributed to the fact that the value of specific heats of the gas differs during both the conditions. At constant volume, the specific heat of the gas is $\dfrac{5}{2}R$ and at constant pressure the specific heat of the gas is $\dfrac{7}{2}R$ .

Formula used: \[\left( a \right)H = n{C_v}\Delta T\]
\[\left( b \right)H = n{C_p}\Delta T\]
Here \[H\] is the heat of combustion, \[{C_v}\] is the specific heat of the gas at constant volume and \[{C_p}\] is the specific heat of the gas at constant pressure and \[\Delta T\] is the change in temperature.

Complete step by step answer:
In this question we have two conditions. One condition is where the volume does not change is an isochoric condition. The other is a condition where the pressure is the same as the isobaric condition. As mentioned before, there will be a difference in the specific heats in both the processes and this will lead to a difference in the heat of combustion of $CO$ .
We will first find the heat of combustion in the condition of constant volume. We know that, \[{C_v} = \dfrac{5}{2}R\], therefore, the answer will be found using the following steps.
$H = {C_v}\Delta T$
$ \Rightarrow \dfrac{5}{2}R \times 300$
substituting the value of gas constant, we get,
$ \Rightarrow \dfrac{5}{2} \times 2 \times 300$
$ \Rightarrow 5 \times 300$
therefore, the answer will be,
\[ \Rightarrow 1500J\]
In the second condition, we have \[{C_p}\] = \[\dfrac{7}{2}R\] , and the heat of combustion will be,
$H = \dfrac{7}{2}R \times 300$
$ \Rightarrow \dfrac{7}{2} \times 2 \times 300$
multiplying both the values,
$ \Rightarrow 7 \times 300$
$ \Rightarrow 2100cal$
Thus, we have found the heat of combustion in both the conditions. It is required to find the difference in the heats. For this we must subtract the heat involved in the second condition from the heat involved in the first condition. This can be demonstrated as follows:
$\Delta H = 2100 - 1500$
$ \Rightarrow 600cal$

So, the correct answer is Option B.

Note: It is also important to remember that for every diatomic gas the \[{C_v} = \dfrac{5}{2}R\] and the ${C_p} = \dfrac{7}{2}R$ . The heat of combustion changes due to the change in specific heats in this way.
The condition where the pressure is constant is called an isobaric condition and the condition where the volume is constant is called an isochoric condition.
Remember to convert the temperature from Celsius scale to kelvin scale in these questions.